# Appendix:Glossary of linear algebra

Definition from Wiktionary, the free dictionary

This is a glossary of linear algebra.

**Table of Contents:** A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

## A[edit]

- affine transformation
- A linear transformation between vector spaces followed by a translation.

## B[edit]

- basis
- In a vector space, a linearly independent set of vectors spanning the whole vector space.

## D[edit]

- determinant
- The unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value of 1 for the unit matrix.

- diagonal matrix
- A matrix in which only the entries on the main diagonal are non-zero.

- dimension
- The number of elements of any basis of a vector space.

## I[edit]

- identity matrix
- A diagonal matrix all of the diagonal elements of which are equal to 1.

- inverse matrix
- Of a matrix A, another matrix B such that A multiplied by B and B multiplied by A both equal the identity matrix.

## L[edit]

- linear algebra
- The branch of mathematics that deals with vectors, vector spaces, linear transformations and systems of linear equations.

- linear combination
- A sum, each of whose summands is an appropriate vector times an appropriate scalar (or ring element).

- linear equation
- A polynomial equation of the first degree (such as x = 2y - 7).

- linear transformation
- A map between vector spaces which respects addition and multiplication.

- linearly independent
- (Of a set of vectors or ring elements) whose nontrivial linear combinations are nonzero.

## M[edit]

- matrix
- A rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory.

## S[edit]

- spectrum
- Of a bounded linear operator
*A*, the scalar values λ such that the operator*A—λI*, where*I*denotes the identity operator, does not have a bounded inverse.

- square matrix
- A matrix having the same number of rows as columns.

## V[edit]

- vector
- A directed quantity, one with both magnitude and direction; an element of a vector space.

- vector space
- A set
*V*, whose elements are called "vectors", together with a binary operation + forming a module (*V*,+), and a set*F*^{*}of bilinear unary functions*f*^{*}:*V*→*V*, each of which corresponds to a "scalar" element*f*of a field*F*, such that the composition of elements of*F*^{*}corresponds isomorphically to multiplication of elements of*F*, and such that for any vector**v**, 1^{*}(**v**) =**v**.