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

Trans. through Richard A. Silverman

The authors start with linear areas, beginning with uncomplicated options and finishing with issues in analytic geometry. They then deal with multilinear types and tensors (linear and bilinear kinds, normal definition of a tensor, algebraic operations on tensors, symmetric and antisymmetric tensors, etc.), and linear transformation (again uncomplicated recommendations, the matrix and multiplication of linear variations, inverse alterations and matrices, teams and subgroups, etc.). The final bankruptcy offers with additional issues within the box: eigenvectors and eigenvalues, matrix ploynomials and the Hamilton-Cayley theorem, relief of a quadratic shape to canonical shape, illustration of a nonsingular transformation, and extra. each one person part — there are 25 in all — encompasses a challenge set, creating a overall of over 250 difficulties, all rigorously chosen and paired. tricks and solutions to lots of the difficulties are available on the finish of the book.

Dr. Silverman has revised the textual content and diverse pedagogical and mathematical advancements, and restyled the language in order that it really is much more readable. With its transparent exposition, many appropriate and engaging difficulties, abundant illustrations, index and bibliography, this publication could be priceless within the school room or for self-study as a great advent to the real topics of linear algebra and tensors.

**Read Online or Download An Introduction to Linear Algebra and Tensors PDF**

**Similar linear books**

**Banach Algebras (Modern Analytic and Computational Methods in Science and Mathematics)**

Banach algebras are Banach areas built with a continuing binary operation of multiplication. a number of areas thought of in practical research also are algebras, e. g. the gap C(0, 1) with pointwise multiplication of services, or the distance l1 with convolution multiplication of sequences. Theorems of the final conception of Banach algebras, utilized to these areas, yield a number of classical result of research, e.

**The Linear Algebra a Beginning Graduate Student Ought to Know, Second Edition**

This e-book conscientiously bargains with the summary concept and, even as, devotes massive house to the numerical and computational facets of linear algebra. It includes a huge variety of thumbnail pix of researchers who've contributed to the advance of linear algebra as we all know it this day and in addition comprises over 1,000 workouts, lots of that are very tough.

**Descriptive Topology and Functional Analysis: In Honour of Jerzy Kakol's 60th Birthday**

Descriptive topology and useful research, with broad fabric demonstrating new connections among them, are the topic of the 1st portion of this paintings. purposes to areas of continuing services, topological Abelian teams, linear topological equivalence and to the separable quotient challenge are integrated and are provided as open difficulties.

- Introduction to Large Truncated Toeplitz Matrices
- Linear Operators in Function Spaces: 12th International Conference on Operator Theory Timişoara (Romania) June 6–16, 1988
- Matrix Analysis and Applied Linear Algebra: Solutions Manual
- Real and Complex Clifford Analysis (Advances in Complex Analysis and Its Applications)

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

**Example text**

Let elye2, e 3 be an orthonormal basis in the space L 3 and let e r , e2,, e3, be another orthonormal e3 basis in L 3, both emanating from the same origin O (see Figure 3). Clearly, the vectors of the “new” basis e r , er , e3, can be expressed as linear com binations of the vectors of the “old” basis et, e2, e3. Let yn denote the coefficient of et. in the expansion of e,, with respect to the old basis vectors. Then the expansions of the new basis vectors with respect to the old basis F igure 3 vectors take the form e r = y i'ie i + 7i'2e2 + 7 i'3e3> er = yr i e, + yr2e2 + yr3e3, e 3' = 7 r ^ l + ?

W) =

More generally, let q>= q>{x, y, z , . . , w) be a multilinear form of degree. Then (p is said to be antisymmetric in two {given) arguments if it changes sign when the two arguments are interchanged. By the same token, the tensor determined by (p is antisymmetric in the corresponding indices. A multilinear form of degree p is said to be antisymmetric (without further qualification) if it changes sign when any two of its arguments are interchanged, and the tensor determined by such a form is called an antisymmetric tensor of order p.