FINITE- DIMENSIONAL VECTOR SPACES SECOND EDITION1958 |
Contents
CHAPTER PAGE | 1 |
Linear dependence 7 6 Linear combinations 9 7 Bases | 8 |
culus of subspaces 17 12 Dimension of a subspace 18 13 Dual | 17 |
Copyright | |
7 other sections not shown
Common terms and phrases
adjoint algebraic multiplicity alternating n-linear form arbitrary assert bilinear called commutative complex numbers complex vector space concept consider coordinate system correspondence coset defined definition denote dependent diagonal dimension direct sum disjoint dual space elements equation exists fact field finite finite-dimensional inner product finite-dimensional vector space follows Hermitian implies inner product space invariant isometry isomorphism k-linear form K₁ linear combination linear functional linear transformation linearly independent M₁ matrix multilinear multilinear form n-dimensional vector space necessary and sufficient nilpotent notation obtain orthogonal orthonormal basis orthonormal set permutation perpendicular projection polynomial proof proper value proper vector properties Prove quotient space real numbers real vector space relation respect result scalar self-adjoint self-adjoint transformation spectral theorem subset subspace spanned sufficient condition Suppose tensor product tion unitary space vectors x1 write y₁ zero