An Introduction to Linear AlgebraCourier Corporation, 1 janv. 1990 - 440 pages Rigorous, self-contained coverage of determinants, vectors, matrices and linear equations, quadratic forms, more. Elementary, easily readable account with numerous examples and problems at the end of each chapter. "The straight-forward clarity of the writing is admirable." — American Mathematical Monthly. Bibliography. |
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Page vi
... linear manifolds 123 4.4 . Further instances of linear operators 126 V. SYSTEMS OF LINEAR EQUATIONS AND RANK OF MATRICES 5.1 . Preliminary results 131 5.2 . The rank theorem 136 5.3 . The general theory of linear equations 5.4 .
... linear manifolds 123 4.4 . Further instances of linear operators 126 V. SYSTEMS OF LINEAR EQUATIONS AND RANK OF MATRICES 5.1 . Preliminary results 131 5.2 . The rank theorem 136 5.3 . The general theory of linear equations 5.4 .
Page vii
... Further theorems on rank of matrices VI . ELEMENTARY OPERATIONS AND THE CONCEPT OF EQUIVALENCE 6.1 . E - operations and E - matrices 6.2 . Equivalent matrices 6.3 . Applications of the preceding theory 6.4 . Congruence transformations ...
... Further theorems on rank of matrices VI . ELEMENTARY OPERATIONS AND THE CONCEPT OF EQUIVALENCE 6.1 . E - operations and E - matrices 6.2 . Equivalent matrices 6.3 . Applications of the preceding theory 6.4 . Congruence transformations ...
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Expressions et termes fréquents
A₁ algebra assertion automorphism B₁ basis bilinear form bilinear operator C₁ canonical forms characteristic roots characteristic vectors coefficients columns commute complex numbers convergent coordinates Deduce defined denote determinant diagonal form diagonal matrix E-operations equal equivalence EXERCISE exists follows functions geometry given Hence hermitian form hermitian matrix identity implies inequality integers invariant space isomorphic linear equations linear manifold linear transformation linearly independent matrix group matrix of order minimum polynomial multiplication non-singular linear transformation non-singular matrix non-zero numbers nxn matrix obtain orthogonal matrix positive definite positive semi-definite possesses problems proof of Theorem prove quadratic form quadric rank relation represented respect result rotation S-¹AS satisfies scalar Show similar skew-symmetric matrix solution square matrix suppose symmetric matrix t₁ theory tion triangular unique unit element unitary matrix V₁ values variables vector space view of Theorem w₁ write x₁ y₁ zero