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BASIC OPERATIONS FOR MATRICES
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a-basis addition algebraic bilinear called canonical form canonical representation canonical set Chap characteristic values characteristic vector coefficients completes the proof complex numbers computation congruence coordinates defined denote detA diagonal representation direct sum echelon system elementary divisors equal equivalence relation Euclidean space example exists field F finite hence Hermitian forms Hermitian function Hermitian matrix implies inner-product function integers invariant factors invariant spaces inverse isomorphism Lemma linear combination linear equations linear forms linear functions linear transformation linearly independent minimum function n-tuples nonzero normal transformation notation null spaces obtain one-one correspondence orthogonal orthonormal basis orthonormal set postulates PROBLEMS proof of Theorem properties prove quadratic form rank real numbers reduces relation matrix relative represented result row transformations row vectors set of vectors Show solution subset subspace symmetric matrix system of linear tion trans unit element unitary space vector space verify Vn(F Vn(R