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VECTOR SPACES AND LINEAR MANIFOLDS
THE ALGEBRA OF MATRICES
11 other sections not shown
algebra assertion assume automorphism bilinear form bilinear operator canonical forms characteristic polynomial characteristic roots characteristic vectors coefficients cofactor commute complement complex numbers consider convergent coordinates corollary to Theorem Deduce defined denote determinant diagonal elements diagonal form diagonal matrix dimensionality equal Exercise follows 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 non-singular linear transformation non-singular matrix numbers nxn matrix obtain orthogonal matrix permutation positive semi-definite possesses power series principal minors proof of Theorem prove quadratic form quadric rank real symmetric reduces represented result rotation scalar Show similar singular skew-symmetric matrix solution square matrix suppose symmetric matrix tion triangular matrix unique unit element unitary matrix vanish variables vector space vectors of order view of Theorem write xrAx xTAx zero