Linear

Get An Introduction to Linear Algebra and Tensors PDF

By M. A. Akivis, V. V. Goldberg, Richard A. Silverman

ISBN-10: 0486635457

ISBN-13: 9780486635453

Trans. by means of Richard A. Silverman

The current ebook, a useful addition to the English-language literature on linear algebra and tensors, constitutes a lucid, eminently readable and fully user-friendly creation to this box of arithmetic. a unique advantage of the booklet is its unfastened use of tensor notation, specifically the Einstein summation conference. The remedy is almost self-contained. in truth, the mathematical historical past assumed at the a part of the reader hardly ever exceeds a smattering of calculus and an informal acquaintance with determinants.
The authors commence with linear areas, beginning with uncomplicated innovations and finishing with themes in analytic geometry. They then deal with multilinear types and tensors (linear and bilinear types, normal definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again simple ideas, the matrix and multiplication of linear modifications, inverse ameliorations and matrices, teams and subgroups, etc.). The final bankruptcy bargains with additional issues within the box: eigenvectors and eigenvalues, matrix ploynomials and the Hamilton-Cayley theorem, aid of a quadratic shape to canonical shape, illustration of a nonsingular transformation, and extra. every one person part — there are 25 in all — features a challenge set, creating a overall of over 250 difficulties, all conscientiously chosen and coupled. tricks and solutions to many of the difficulties are available on the finish of the book.
Dr. Silverman has revised the textual content and various pedagogical and mathematical advancements, and restyled the language in order that it truly is much more readable. With its transparent exposition, many correct and engaging difficulties, plentiful illustrations, index and bibliography, this ebook may be worthwhile within the school room or for self-study as an exceptional advent to the $64000 matters of linear algebra and tensors.

Show description

Read or Download An Introduction to Linear Algebra and Tensors PDF

Best linear books

Constructions of Lie Algebras and their Modules - download pdf or read online

This ebook bargains with relevant uncomplicated Lie algebras over arbitrary fields of attribute 0. It goals to offer buildings of the algebras and their finite-dimensional modules in phrases which are rational with recognize to the given flooring box. All isotropic algebras with non-reduced relative root platforms are taken care of, in addition to classical anisotropic algebras.

Generalized Lie Theory in Mathematics, Physics and Beyond - download pdf or read online

The aim of this ebook is to increase the certainty of the basic function of generalizations of Lie concept and similar non-commutative and non-associative constructions in arithmetic and physics. This quantity is dedicated to the interaction among a number of quickly increasing examine fields in modern arithmetic and physics interested by generalizations of the most buildings of Lie concept geared toward quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative buildings, activities of teams and semi-groups, non-commutative dynamics, non-commutative geometry and purposes in physics and past.

New PDF release: Clifford algebras and spinor structures : a special volume

This quantity is devoted to the reminiscence of Albert Crumeyrolle, who died on June 17, 1992. In organizing the quantity we gave precedence to: articles summarizing Crumeyrolle's personal paintings in differential geometry, normal relativity and spinors, articles which offer the reader an idea of the intensity and breadth of Crumeyrolle's learn pursuits and effect within the box, articles of excessive medical caliber which might be of common curiosity.

Additional resources for An Introduction to Linear Algebra and Tensors

Sample text

3. The definition of a multilinear form q> = (p(x, y, z , . . , w , . . , the value of tp depends only on the values of its vector arguments. For example, a trilinear form (p = (p{x, y, z) depends only on the values of the vectors x, y, z and not on the components of x, y, z relative to any underlying basis e2, e3. In the language o f p. 25, we can say that multilinear forms have been defined in an invariant fashion. Since the components of a vector change in transforming to a new basis, the same must be true of the coefficients of a multilinear form (if the form itself is to remain invariant).

Proof For simplicity, consider the special case p = 3, q = 2, where the set of numbers (1) is of the form aijklm. Suppose the quantity = S ijk a ijk lm h m is a tensor whenever tlrr is a tensor. Let tlm = utvm (the product of two arbitrary vectors ut and vm). Then S ijk = a iJ k lm U i°m '> and contracting this expression with arbitrary vectors x n y p z k, we get W A = *iJkimXiyJZkUiVm. 54 CHAP. 2 MULTILINEAR FORMS AND TENSORS Since siJk is a tensor, the expression on the left is a scalar. It follows that the expression on the right, which depends linearly on the compo­ nents of the vectors x, y, z, u, v, is a multilinear form of degree 5.

If two conditions of the form 1 2 ) 0 >(x, y, z t + z2, . . , w) = p(x, y, z„ . . , w) + (x, y, Az,. . , w) = Ap(x, y, z, . . , w) hold for each of the arguments x, y, z , . . , w. The number of arguments p is called the degree of the multilinear form, and

Download PDF sample

An Introduction to Linear Algebra and Tensors by M. A. Akivis, V. V. Goldberg, Richard A. Silverman


by Daniel
4.0

Rated 4.72 of 5 – based on 25 votes