Vectors, pure and applied :: a general introduction to linear algebra /
"Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysi...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge :
Cambridge University Press,
2013.
|
| Schlagworte: | |
| Online-Zugang: | DE-862 DE-863 |
| Zusammenfassung: | "Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"-- |
| Beschreibung: | 1 online resource (xii, 444 pages) : illustrations |
| Bibliographie: | Includes bibliographical references and index. |
| ISBN: | 9781139626156 1139626159 9781139520034 1139520032 9781283871006 1283871009 9781139622431 1139622439 9781139616850 1139616854 1107238277 9781107238275 1107255023 9781107255029 1139611275 9781139611275 1139613138 9781139613132 |
Internformat
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| 100 | 1 | |a Körner, T. W. |q (Thomas William), |d 1946- |e author. |1 https://id.oclc.org/worldcat/entity/E39PBJgCF6MJtgDD4fgfPWrQbd |0 http://id.loc.gov/authorities/names/n85062597 | |
| 245 | 1 | 0 | |a Vectors, pure and applied : |b a general introduction to linear algebra / |c T.W. Körner. |
| 260 | |a Cambridge : |b Cambridge University Press, |c 2013. | ||
| 300 | |a 1 online resource (xii, 444 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | 0 | |g Part I. |t Familiar vector spaces -- |g 1. |t Gaussian elimination -- |t Two hundred years of algebra -- |t Computational matters -- |t Detached coefficients -- |t Another fifty years -- |g 2. |t A little geometry -- |t Geometric vectors -- |t Higher dimensions -- |t Euclidean distance -- |t Geometry, plane and solid -- |g 3. |t The algebra of square matrices -- |t The summation convention -- |t Multiplying matrices -- |t More algebra for square matrices -- |t Decomposition into elementary matrices -- |t Calculating the inverse -- |g 4. |t The secret life of determinants -- |t The area of a parallelogram -- |t Rescaling -- |t 3 x 3 determinants -- |t Determinants of n × n matrices -- |t Calculating determinants -- |g 5. |t Abstract vector spaces -- |t The space Cn -- |t Abstract vector spaces -- |t Linear maps -- |t Dimension -- |t Image and kernel -- |t Secret sharing -- |g 6. |t Linear maps from Fn to itself -- |t Linear maps, bases and matrices -- |t Eigenvectors and eigenvalues -- |t Diagonalisation and eigenvectors -- |t Linear maps from C2to itself -- |t Diagonalising square matrices -- |t Iteration's artful aid -- |t LU factorisation -- |g 7. |t Distance preserving linear maps -- |t Orthonormal bases -- |t Orthogonal maps and matrices -- |t Rotations and reflections in R2and R3 -- |t Reflections in Rn -- |t QR factorisation -- |g 8. |t Diagonalisation for orthonormal bases -- |t Symmetric maps -- |t Eigenvectors for symmetric linear maps -- |t Stationary points -- |t Complex inner product -- |g 9. |t Cartesian tensors -- |t Physical vectors -- |t General Cartesian tensors -- |t More examples -- |t The vector product -- |g 10. |t More on tensors -- |t Some tensorial theorems -- |t A (very) little mechanics -- |t Left-hand, right-hand -- |t General tensors -- |g Part II. |t General vector spaces -- |g 11. |t Spaces of linear maps -- |t A look at L(U, V) -- |t A look at L(U, U) -- |t Duals (almost) without using bases -- |t Duals using bases -- |g 12. |t Polynomials in L(U, U) -- |t Direct sums -- |t The Cayley-Hamilton theorem -- |t Minimal polynomials -- |t The Jordan normal form -- |t Applications -- |g 13. |t Vector spaces without distances -- |t A little philosophy -- |t Vector spaces over fields -- |t Error correcting codes -- |g 14. |t Vector spaces with distances -- |t Orthogonal polynomials -- |t Inner products and dual spaces -- |t Complex inner product spaces -- |g 15. |t More distances -- |t Distance on L(U, U) -- |t Inner products and triangularisation -- |t The spectral radius -- |t Normal maps -- |g 16. |t Quadratic forms and their relatives -- |t Bilinear forms -- |t Rank and signature -- |t Positive definiteness -- |t Antisymmetric bilinear forms -- |t Further exercises. |
| 520 | |a "Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"-- |c Provided by publisher. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Vector algebra. |0 http://id.loc.gov/authorities/subjects/sh85142448 | |
| 650 | 0 | |a Algebras, Linear. |0 http://id.loc.gov/authorities/subjects/sh85003441 | |
| 650 | 6 | |a Algèbre vectorielle. | |
| 650 | 6 | |a Algèbre linéaire. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x General. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x General. |2 bisacsh | |
| 650 | 7 | |a Álgebra lineal |2 embne | |
| 650 | 7 | |a Álgebra vectorial |2 embne | |
| 650 | 7 | |a Algebras, Linear |2 fast | |
| 650 | 7 | |a Vector algebra |2 fast | |
| 655 | 0 | |a Electronic books. | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Körner, T.W. (Thomas William), 1946- |t Vectors, pure and applied. |d Cambridge : Cambridge University Press, 2013 |z 9781107033566 |w (DLC) 2012036797 |w (OCoLC)809611894 |
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Datensatz im Suchindex
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| _version_ | 1826941996199051264 |
| adam_text | |
| any_adam_object | |
| author | Körner, T. W. (Thomas William), 1946- |
| author_GND | http://id.loc.gov/authorities/names/n85062597 |
| author_facet | Körner, T. W. (Thomas William), 1946- |
| author_role | aut |
| author_sort | Körner, T. W. 1946- |
| author_variant | t w k tw twk |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA200 |
| callnumber-raw | QA200 .K67 2013eb |
| callnumber-search | QA200 .K67 2013eb |
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| contents | Familiar vector spaces -- Gaussian elimination -- Two hundred years of algebra -- Computational matters -- Detached coefficients -- Another fifty years -- A little geometry -- Geometric vectors -- Higher dimensions -- Euclidean distance -- Geometry, plane and solid -- The algebra of square matrices -- The summation convention -- Multiplying matrices -- More algebra for square matrices -- Decomposition into elementary matrices -- Calculating the inverse -- The secret life of determinants -- The area of a parallelogram -- Rescaling -- 3 x 3 determinants -- Determinants of n × n matrices -- Calculating determinants -- Abstract vector spaces -- The space Cn -- Linear maps -- Dimension -- Image and kernel -- Secret sharing -- Linear maps from Fn to itself -- Linear maps, bases and matrices -- Eigenvectors and eigenvalues -- Diagonalisation and eigenvectors -- Linear maps from C2to itself -- Diagonalising square matrices -- Iteration's artful aid -- LU factorisation -- Distance preserving linear maps -- Orthonormal bases -- Orthogonal maps and matrices -- Rotations and reflections in R2and R3 -- Reflections in Rn -- QR factorisation -- Diagonalisation for orthonormal bases -- Symmetric maps -- Eigenvectors for symmetric linear maps -- Stationary points -- Complex inner product -- Cartesian tensors -- Physical vectors -- General Cartesian tensors -- More examples -- The vector product -- More on tensors -- Some tensorial theorems -- A (very) little mechanics -- Left-hand, right-hand -- General tensors -- General vector spaces -- Spaces of linear maps -- A look at L(U, V) -- A look at L(U, U) -- Duals (almost) without using bases -- Duals using bases -- Polynomials in L(U, U) -- Direct sums -- The Cayley-Hamilton theorem -- Minimal polynomials -- The Jordan normal form -- Applications -- Vector spaces without distances -- A little philosophy -- Vector spaces over fields -- Error correcting codes -- Vector spaces with distances -- Orthogonal polynomials -- Inner products and dual spaces -- Complex inner product spaces -- More distances -- Distance on L(U, U) -- Inner products and triangularisation -- The spectral radius -- Normal maps -- Quadratic forms and their relatives -- Bilinear forms -- Rank and signature -- Positive definiteness -- Antisymmetric bilinear forms -- Further exercises. |
| ctrlnum | (OCoLC)821617863 |
| dewey-full | 516/.182 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.182 |
| dewey-search | 516/.182 |
| dewey-sort | 3516 3182 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| genre | Electronic books. |
| genre_facet | Electronic books. |
| id | ZDB-4-EBA-ocn821617863 |
| illustrated | Illustrated |
| indexdate | 2025-03-18T14:20:59Z |
| institution | BVB |
| isbn | 9781139626156 1139626159 9781139520034 1139520032 9781283871006 1283871009 9781139622431 1139622439 9781139616850 1139616854 1107238277 9781107238275 1107255023 9781107255029 1139611275 9781139611275 1139613138 9781139613132 |
| language | English |
| oclc_num | 821617863 |
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| owner_facet | MAIN DE-862 DE-BY-FWS DE-863 DE-BY-FWS |
| physical | 1 online resource (xii, 444 pages) : illustrations |
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| publishDate | 2013 |
| publishDateSearch | 2013 |
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| publisher | Cambridge University Press, |
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| spelling | Körner, T. W. (Thomas William), 1946- author. https://id.oclc.org/worldcat/entity/E39PBJgCF6MJtgDD4fgfPWrQbd http://id.loc.gov/authorities/names/n85062597 Vectors, pure and applied : a general introduction to linear algebra / T.W. Körner. Cambridge : Cambridge University Press, 2013. 1 online resource (xii, 444 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Includes bibliographical references and index. Part I. Familiar vector spaces -- 1. Gaussian elimination -- Two hundred years of algebra -- Computational matters -- Detached coefficients -- Another fifty years -- 2. A little geometry -- Geometric vectors -- Higher dimensions -- Euclidean distance -- Geometry, plane and solid -- 3. The algebra of square matrices -- The summation convention -- Multiplying matrices -- More algebra for square matrices -- Decomposition into elementary matrices -- Calculating the inverse -- 4. The secret life of determinants -- The area of a parallelogram -- Rescaling -- 3 x 3 determinants -- Determinants of n × n matrices -- Calculating determinants -- 5. Abstract vector spaces -- The space Cn -- Abstract vector spaces -- Linear maps -- Dimension -- Image and kernel -- Secret sharing -- 6. Linear maps from Fn to itself -- Linear maps, bases and matrices -- Eigenvectors and eigenvalues -- Diagonalisation and eigenvectors -- Linear maps from C2to itself -- Diagonalising square matrices -- Iteration's artful aid -- LU factorisation -- 7. Distance preserving linear maps -- Orthonormal bases -- Orthogonal maps and matrices -- Rotations and reflections in R2and R3 -- Reflections in Rn -- QR factorisation -- 8. Diagonalisation for orthonormal bases -- Symmetric maps -- Eigenvectors for symmetric linear maps -- Stationary points -- Complex inner product -- 9. Cartesian tensors -- Physical vectors -- General Cartesian tensors -- More examples -- The vector product -- 10. More on tensors -- Some tensorial theorems -- A (very) little mechanics -- Left-hand, right-hand -- General tensors -- Part II. General vector spaces -- 11. Spaces of linear maps -- A look at L(U, V) -- A look at L(U, U) -- Duals (almost) without using bases -- Duals using bases -- 12. Polynomials in L(U, U) -- Direct sums -- The Cayley-Hamilton theorem -- Minimal polynomials -- The Jordan normal form -- Applications -- 13. Vector spaces without distances -- A little philosophy -- Vector spaces over fields -- Error correcting codes -- 14. Vector spaces with distances -- Orthogonal polynomials -- Inner products and dual spaces -- Complex inner product spaces -- 15. More distances -- Distance on L(U, U) -- Inner products and triangularisation -- The spectral radius -- Normal maps -- 16. Quadratic forms and their relatives -- Bilinear forms -- Rank and signature -- Positive definiteness -- Antisymmetric bilinear forms -- Further exercises. "Many books in linear algebra focus purely on getting students through exams, but this text explains both the how and the why of linear algebra and enables students to begin thinking like mathematicians. The author demonstrates how different topics (geometry, abstract algebra, numerical analysis, physics) make use of vectors in different ways and how these ways are connected, preparing students for further work in these areas. The book is packed with hundreds of exercises ranging from the routine to the challenging. Sketch solutions of the easier exercises are available online"-- Provided by publisher. Print version record. English. Vector algebra. http://id.loc.gov/authorities/subjects/sh85142448 Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre vectorielle. Algèbre linéaire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Geometry General. bisacsh Álgebra lineal embne Álgebra vectorial embne Algebras, Linear fast Vector algebra fast Electronic books. Print version: Körner, T.W. (Thomas William), 1946- Vectors, pure and applied. Cambridge : Cambridge University Press, 2013 9781107033566 (DLC) 2012036797 (OCoLC)809611894 |
| spellingShingle | Körner, T. W. (Thomas William), 1946- Vectors, pure and applied : a general introduction to linear algebra / Familiar vector spaces -- Gaussian elimination -- Two hundred years of algebra -- Computational matters -- Detached coefficients -- Another fifty years -- A little geometry -- Geometric vectors -- Higher dimensions -- Euclidean distance -- Geometry, plane and solid -- The algebra of square matrices -- The summation convention -- Multiplying matrices -- More algebra for square matrices -- Decomposition into elementary matrices -- Calculating the inverse -- The secret life of determinants -- The area of a parallelogram -- Rescaling -- 3 x 3 determinants -- Determinants of n × n matrices -- Calculating determinants -- Abstract vector spaces -- The space Cn -- Linear maps -- Dimension -- Image and kernel -- Secret sharing -- Linear maps from Fn to itself -- Linear maps, bases and matrices -- Eigenvectors and eigenvalues -- Diagonalisation and eigenvectors -- Linear maps from C2to itself -- Diagonalising square matrices -- Iteration's artful aid -- LU factorisation -- Distance preserving linear maps -- Orthonormal bases -- Orthogonal maps and matrices -- Rotations and reflections in R2and R3 -- Reflections in Rn -- QR factorisation -- Diagonalisation for orthonormal bases -- Symmetric maps -- Eigenvectors for symmetric linear maps -- Stationary points -- Complex inner product -- Cartesian tensors -- Physical vectors -- General Cartesian tensors -- More examples -- The vector product -- More on tensors -- Some tensorial theorems -- A (very) little mechanics -- Left-hand, right-hand -- General tensors -- General vector spaces -- Spaces of linear maps -- A look at L(U, V) -- A look at L(U, U) -- Duals (almost) without using bases -- Duals using bases -- Polynomials in L(U, U) -- Direct sums -- The Cayley-Hamilton theorem -- Minimal polynomials -- The Jordan normal form -- Applications -- Vector spaces without distances -- A little philosophy -- Vector spaces over fields -- Error correcting codes -- Vector spaces with distances -- Orthogonal polynomials -- Inner products and dual spaces -- Complex inner product spaces -- More distances -- Distance on L(U, U) -- Inner products and triangularisation -- The spectral radius -- Normal maps -- Quadratic forms and their relatives -- Bilinear forms -- Rank and signature -- Positive definiteness -- Antisymmetric bilinear forms -- Further exercises. Vector algebra. http://id.loc.gov/authorities/subjects/sh85142448 Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre vectorielle. Algèbre linéaire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Geometry General. bisacsh Álgebra lineal embne Álgebra vectorial embne Algebras, Linear fast Vector algebra fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85142448 http://id.loc.gov/authorities/subjects/sh85003441 |
| title | Vectors, pure and applied : a general introduction to linear algebra / |
| title_alt | Familiar vector spaces -- Gaussian elimination -- Two hundred years of algebra -- Computational matters -- Detached coefficients -- Another fifty years -- A little geometry -- Geometric vectors -- Higher dimensions -- Euclidean distance -- Geometry, plane and solid -- The algebra of square matrices -- The summation convention -- Multiplying matrices -- More algebra for square matrices -- Decomposition into elementary matrices -- Calculating the inverse -- The secret life of determinants -- The area of a parallelogram -- Rescaling -- 3 x 3 determinants -- Determinants of n × n matrices -- Calculating determinants -- Abstract vector spaces -- The space Cn -- Linear maps -- Dimension -- Image and kernel -- Secret sharing -- Linear maps from Fn to itself -- Linear maps, bases and matrices -- Eigenvectors and eigenvalues -- Diagonalisation and eigenvectors -- Linear maps from C2to itself -- Diagonalising square matrices -- Iteration's artful aid -- LU factorisation -- Distance preserving linear maps -- Orthonormal bases -- Orthogonal maps and matrices -- Rotations and reflections in R2and R3 -- Reflections in Rn -- QR factorisation -- Diagonalisation for orthonormal bases -- Symmetric maps -- Eigenvectors for symmetric linear maps -- Stationary points -- Complex inner product -- Cartesian tensors -- Physical vectors -- General Cartesian tensors -- More examples -- The vector product -- More on tensors -- Some tensorial theorems -- A (very) little mechanics -- Left-hand, right-hand -- General tensors -- General vector spaces -- Spaces of linear maps -- A look at L(U, V) -- A look at L(U, U) -- Duals (almost) without using bases -- Duals using bases -- Polynomials in L(U, U) -- Direct sums -- The Cayley-Hamilton theorem -- Minimal polynomials -- The Jordan normal form -- Applications -- Vector spaces without distances -- A little philosophy -- Vector spaces over fields -- Error correcting codes -- Vector spaces with distances -- Orthogonal polynomials -- Inner products and dual spaces -- Complex inner product spaces -- More distances -- Distance on L(U, U) -- Inner products and triangularisation -- The spectral radius -- Normal maps -- Quadratic forms and their relatives -- Bilinear forms -- Rank and signature -- Positive definiteness -- Antisymmetric bilinear forms -- Further exercises. |
| title_auth | Vectors, pure and applied : a general introduction to linear algebra / |
| title_exact_search | Vectors, pure and applied : a general introduction to linear algebra / |
| title_full | Vectors, pure and applied : a general introduction to linear algebra / T.W. Körner. |
| title_fullStr | Vectors, pure and applied : a general introduction to linear algebra / T.W. Körner. |
| title_full_unstemmed | Vectors, pure and applied : a general introduction to linear algebra / T.W. Körner. |
| title_short | Vectors, pure and applied : |
| title_sort | vectors pure and applied a general introduction to linear algebra |
| title_sub | a general introduction to linear algebra / |
| topic | Vector algebra. http://id.loc.gov/authorities/subjects/sh85142448 Algebras, Linear. http://id.loc.gov/authorities/subjects/sh85003441 Algèbre vectorielle. Algèbre linéaire. MATHEMATICS Algebra General. bisacsh MATHEMATICS Geometry General. bisacsh Álgebra lineal embne Álgebra vectorial embne Algebras, Linear fast Vector algebra fast |
| topic_facet | Vector algebra. Algebras, Linear. Algèbre vectorielle. Algèbre linéaire. MATHEMATICS Algebra General. MATHEMATICS Geometry General. Álgebra lineal Álgebra vectorial Algebras, Linear Vector algebra Electronic books. |
| work_keys_str_mv | AT kornertw vectorspureandappliedageneralintroductiontolinearalgebra |