Linear algebra

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Bibliographic Details
Main Author Shilov, G. E.
Format Electronic eBook
LanguageEnglish
Published New York : Dover Publications, 1977.
EditionRev. English ed. /
SeriesDover books on mathematics.
Subjects
Algebras, Linear.
elektronické knihy
electronic books
Online AccessFull text
ISBN9781621985839
1621985830
048663518X
9780486635187
Physical Description1 online resource (xi, 387 pages) : graphs

Cover

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100 1 |a Shilov, G. E.  |q (Georgiĭ Evgenʹevich)  |1 https://id.oclc.org/worldcat/entity/E39PBJdRC98BDgX6rRvTYCj3cP 
245 1 0 |a Linear algebra /  |c Georgi E. Shilov. 
250 |a Rev. English ed. /  |b translated and edited by Richard A. Silverman. 
260 |a New York :  |b Dover Publications,  |c 1977. 
300 |a 1 online resource (xi, 387 pages) :  |b graphs 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a Dover books on mathematics. 
500 |a Original ed. published by Prentice-Hall, Englewood Cliffs, N.J. 
504 |a Includes bibliographical references (page 379) and index. 
505 0 |a Machine derived contents note: chapter 1 -- Determinants -- 1.1. Number Fields -- 1.2. Problems of the Theory of Systems of Linear Equations -- 1.3. Determinants of Order n -- 1.4. Properties of Determinants -- 1.5. Cofactors and Minors -- 1.6. Practical Evaluation of Determinants -- 1.7. Cramer's Rule -- 1.8. Minors of Arbitrary Order. Laplace's Theorem -- 1.9. Linear Dependence between Columns -- Problems -- chapter 2 -- Linear Spaces -- 2.1. Definitions -- 2.2. Linear Dependence -- 2.3. "Bases, Components, Dimension" -- 2.4. Subspaces -- 2.5. Linear Manifolds -- 2.6. Hyperplanes -- 2.7. Morphisms of Linear Spaces -- Problems -- chapter 3 -- Systems Of Linear Equations -- 3.1. More on the Rank of a Matrix -- 3.2. Nontrivial Compatibility of a Homogeneous Linear System -- 3.3. The Compatability Condition for a General Linear System -- 3.4. The General Solution of a Linear System -- 3.5. Geometric Properties of the Solution Space -- 3.6. Methods for Calculating the Rank of a Matrix -- Problems -- chapter 4 -- Linear Functions Of A Vector Argument -- 4.1. Linear Forms -- 4.2. Linear Operators -- 4.3. Sums and Products of Linear Operators -- 4.4. Corresponding Operations on Matrices -- 4.5. Further Properties of Matrix Multiplication -- 4.6. The Range and Null Space of a Linear Operator -- 4.7. Linear Operators Mapping a Space Kn into Itself -- 4.8. Invariant Subspaces -- 4.9. Eigenvectors and Eigenvalues -- Problems -- chapter 5 -- Coordinate Transformations -- 5.1. Transformation to a New Basis -- 5.2. Consecutive Transformations -- 5.3. Transformation of the Components of a Vector -- 5.4. Transformation of the Coefficients of a Linear Form -- 5.5. Transformation of the Matrix of a Linear Operator -- 5.6. Tensors -- Problems -- chapter 6 -- The Canonical Form Of The Matrix Of A Linear Operator -- 6.1. Canonical Form of the Matrix of a Nilpotent Operator -- 6.2. Algebras. The Algebra of Polynomials -- 6.3. Canonical Form of the Matrix of an Arbitrary Operator -- 6.4. Elementary Divisors -- 6.5. Further Implications -- 6.6. The Real Jordan Canonical Form -- 6.7. "Spectra, Jets and Polynomials" -- 6.8. Operator Functions and Their Matrices -- Problems -- chapter 7 -- Bilinear And Quadratic Forms -- 7.1. Bilinear Forms -- 7.2. Quadratic Forms -- 7.3. Reduction of a Quadratic Form to Canonical Form -- 7.4. The Canonical Basis of a Bilinear Form -- 7.5. Construction of a Canonical Basis by Jacobi's Method -- 7.6. Adjoint Linear Operators -- 7.7. Isomorphism of Spaces Equipped with a Bilinear Form -- 7.8. Multilinear Forms -- 7.9. Bilinear and Quadratic Forms in a Real Space -- Problems -- chapter 8 -- Euclidean Spaces -- 8.1. Introduction -- 8.2. Definition of a Euclidean Space -- 8.3. Basic Metric Concepts -- 8.4. Orthogonal Bases -- 8.5. Perpendiculars -- 8.6. The Orthogonalization Theorem -- 8.7. The Gram Determinant -- 8.8. Incompatible Systems and the Method of Least Squares -- 8.9. Adjoint Operators and Isometry -- Problems -- chapter 9 -- Unitary Spaces -- 9.1. Hermitian Forms -- 9.2. The Scalar Product in a Complex Space -- 9.3. Normal Operators -- 9.4. Applications to Operator Theory in Euclidean Space -- Problems -- chapter 10 -- Quadratic Forms In Euclidean And Unitary Spaces -- 10.1. Basic Theorem on Quadratic Forms in a Euclidean Space -- 10.2. Extremal Properties of a Quadratic Form -- 10.3 Simultaneous Reduction of Two Quadratic Forms -- 10.4. Reduction of the General Equation of a Quadratic Surface -- 10.5. Geometric Properties. 
506 |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty 
590 |a Knovel  |b Knovel (All titles) 
650 0 |a Algebras, Linear. 
655 7 |a elektronické knihy  |7 fd186907  |2 czenas 
655 9 |a electronic books  |2 eczenas 
776 0 8 |i Print version:  |w (DLC) 77075267  |w (OCoLC)3447101 
830 0 |a Dover books on mathematics. 
856 4 0 |u https://proxy.k.utb.cz/login?url=https://app.knovel.com/hotlink/toc/id:kpLA000001/linear-algebra?kpromoter=marc  |y Full text 

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