Lectures on Linear AlgebraCourier Corporation, 1 de gen. 1989 - 185 pàgines Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector. |
Continguts
nDimensional Spaces Linear and Bilinear Forms | 1 |
Euclidean space | 14 |
Orthogonal basis Isomorphism of Euclidean spaces | 21 |
Bilinear and quadratic forms | 34 |
Reduction of a quadratic form to a sum of squares | 42 |
Reduction of a quadratic form by means of a triangular trans formation | 46 |
The law of inertia | 55 |
Complex ndimensional space | 60 |
Unitary transformations | 103 |
Commutative linear transformations Normal transformations | 107 |
Decomposition of a linear transformation into a product of a unitary and selfadjoint transformation | 111 |
Linear transformations on a real Euclidean space | 114 |
Extremal properties of eigenvalues | 126 |
The Canonical Form of an Arbitrary Linear Transformation | 132 |
Reduction to canonical form | 137 |
Elementary divisors | 142 |
Linear Transformations | 70 |
Invariant subspaces Eigenvalues and eigenvectors of a linear transformation | 81 |
The adjoint of a linear transformation | 90 |
Selfadjoint Hermitian transformations Simultaneous reduc tion of a pair of quadratic forms to a sum of squares | 97 |
Polynomial matrices | 149 |
Introduction to Tensors | 164 |
Tensors | 171 |
Altres edicions - Mostra-ho tot
Frases i termes més freqüents
a₁ Ae₁ arbitrary basis e₁ basis relative basis vectors characteristic polynomial choice of basis coefficients column complex numbers compute coordinates corresponding defined diagonal form dimension dual e₂ eigenvalues eigenvector elementary divisors elementary transformations elements Euclidean space Example EXERCISE exists f₁ f₂ follows form A(x geometry Hence implies inner product invariant subspace inverse isomorphism Jordan canonical form kth order minors Lemma Let e₁ linear combination linear function linear transformation linearly independent linearly independent vectors mathematics matrix ax multilinear function multiplication n-dimensional space n-dimensional vector space n-tuples n₁ necessary and sufficient nnen non-singular non-zero number of linearly orthogonal basis orthogonal transformation orthonormal basis polynomial matrix polynomials of degree positive definite problems proof prove quadratic form real numbers scalar self-adjoint transformation set of vectors subspace R₁ sum of squares tensor of rank theorem theory tion unitary transformation vectors e₁ y₁
Referències a aquest llibre
Co-integration, Error Correction, and the Econometric Analysis of Non ... Anindya Banerjee Previsualització no disponible - 1993 |