# Appendix:Glossary of linear algebra

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

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

## B

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

## D

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

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

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

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

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

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*:VV, 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.