Linear Algebra and Matrix TheoryAdvanced undergraduate and first-year graduate students have long regarded this text as one of the best available works on matrix theory in the context of modern algebra. Teachers and students will find it particularly suited to bridging the gap between ordinary undergraduate mathematics and completely abstract mathematics. The first five chapters treat topics important to economics, psychology, statistics, physics, and mathematics. Subjects include equivalence relations for matrixes, postulational approaches to determinants, and bilinear, quadratic, and Hermitian forms in their natural settings. The final chapters apply chiefly to students of engineering, physics, and advanced mathematics. They explore groups and rings, canonical forms for matrixes with respect to similarity via representations of linear transformations, and unitary and Euclidean vector spaces. Numerous examples appear throughout the text. |
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a-basis addition algebraic bilinear called canonical form canonical representation canonical set Chap characteristic values characteristic vector coeflicient 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 final find first fixed hence 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 positive definite postulates PROBLEMS proof of Theorem properties prove quadratic form rank real numbers reduces relation matrix relative represented result row transformations row vectors satisfies set of vectors Show solution subset subspace symmetric matrix system of linear tion unit element unitary space vector space verify