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

ISBN-10: 0486635457

ISBN-13: 9780486635453

Trans. by way of Richard A. Silverman

The authors start with linear areas, beginning with easy innovations and finishing with themes in analytic geometry. They then deal with multilinear varieties and tensors (linear and bilinear types, normal definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again easy innovations, the matrix and multiplication of linear variations, 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. each one person part — there are 25 in all — incorporates a challenge set, creating a overall of over 250 difficulties, all conscientiously chosen and coupled. tricks and solutions to lots 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 suitable and fascinating difficulties, plentiful illustrations, index and bibliography, this ebook could be precious within the school room or for self-study as a good creation to the real matters of linear algebra and tensors.

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**Additional info for An Introduction to Linear Algebra and Tensors**

**Sample text**

The operation leading from the bilinear form (p to the bilinear form (px is called symmetrization of tp, while the operation leading from q>to tp2 is called antisymmetrization of q>. (x, y) +

Relative to a new orthonormal basis ©i'> >e 3 '> ^ e form

(ee, e,<). But e,- = in going over to the new basis. *,’ «/) = leitrPu • Hence the coefficients of the bilinear form (p transform according to the law af f = J e ffrfiu - (2) Note the deep similarity between (2) and the transformation law (2), p. 39, for a linear form. Conversely we have the following T heorem . I f the elements aij o f the matrix (1) transform according to the law (2) under a basis transformation in L 3, then A is the matrix associated with a bilinear form.

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

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

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