An Introduction to Linear Algebra

addition assertion associated assume basis bilinear form called characteristic roots characteristic vectors classes coefficients columns complex consider consisting convergent coordinates COROLLARY corresponding course Deduce defined denote dependent determinant diagonal diagonal matrix discussion distinct elements equal equation equivalence established EXERCISE exists expressed fact Find follows functions further given Hence hermitian form identity implies inequality invariant isomorphic least linear manifold linear transformation linearly independent means minor multiplication negative non-singular non-zero normal nxn matrix obtain obvious once operator orthogonal matrix polynomial positive definite possesses principal problem proof proper properties prove quadratic form rank reduces relation represented respect result rotation rows satisfies scalar Show similar singular solution square suppose symmetric symmetric matrix Theorem theory tions triangular unique unit unitary values variables vector space write zero