A Course in Linear Algebra

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Harcourt Brace Jovanvich, Jan 1, 1988 - Mathematics - 434 pages
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Contents

Vector Spaces
1
Linear Transformations
62
The Determinant Function
133
Copyright

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additive inverse algebra basis vectors bijective block matrices canonical basis Cauchy-Schwarz inequality Cayley-Hamilton theorem change of basis Chapter characteristic polynomial coefficients column complex numbers compute conic section consider continuous functions contrapositive coordinate coordinate axis coordinate vector Corollary Cramer's rule cycle cyclic subspaces defined Definition denoted det(A determinant diagonal entries diagonal matrix diagonalizable diagonalizable matrix difference equations differential dim(V dim(W dimension direct sum distinct eigenvalues dot product eachy echelon form eigenfunctions eigenspace eigenvalue X eigenvalues eigenvectors elementary matrices Example Exercise finite set finite-dimensional vector space free variables function geometric Gram-Schmidt process Hence Hermitian inner product Hessian matrix However identity element identity matrix independent set induction injective injective and surjective inner product space integer invariant subspace inverse function invertible invertible matrix isomorphism Jim Rice Jordan block Jordan canonical form Jordan form Legendre polynomials Let W linear algebra linear combination linear differential equations linear equations linear mapping linear transformation linearly independent mathematical induction matrix multiplication matrix product minimal polynomial multilinear n x n n x n matrix nilpotent nonzero normal matrix obtain operations ordered pairs ordinary differential equation orthogonal orthogonal matrix orthogonal projection orthonormal basis parallelepiped parallelogram polarization identity positive-definite proof properties Proposition Prove quadratic form quadric surfaces real numbers roots rotation matrix satisfies scalar multiplication Section self-adjoint set of solutions set of vectors Show similar matrices skew-symmetric solving Span Span(S spanning set spectral theorem standard basis statement subset subspace surjective symmetric symmetric matrix system of equations Thus triangle inequality triangular matrix unique unit vector vector subspace vector sum vector x wave equation well-ordering property zero zero vector

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