An Introduction to Linear Algebra
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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algebra assertion assume automorphism bilinear form bilinear operator canonical forms characteristic polynomial characteristic roots characteristic vectors coefficients cofactor columns commute complex numbers convergent coordinates corollary to Theorem Deduce defined denote determinant diagonal elements diagonal form diagonal matrix dimensionality equal EXERCISE follows geometry Hence hermitian form hermitian matrix identity implies inequality integers inverse isomorphic linear combination linear equations linear manifold linear transformation linearly independent matrix group matrix of order minimum polynomial multiplication n x n non-singular linear transformation non-singular matrix numbers nxn matrix obtain orthogonal matrix permutation positive semi-definite possesses problems proof of Theorem prove quadratic form quadric rank real symmetric reduces represented respect result rotation scalar Show similar singular solution square matrix suppose symmetric matrix theory tions triangular matrix unique unit element unitary matrix vanish variables vector space vectors of order view of Theorem write xrAx xrBx zero