# Linear Algebra/Glossary

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## A

[edit | edit source]- adjugate
- Also called
**classical adjoint**. The matrix adj*A*formed from a square matrix*A*by replacing the (*i, j*)-entry of*A*by the (*i, j*)-cofactor, for all*i*and*j*, and then transposing the resulting matrix. - affine transformation
- A mapping of the form , with
*A*an matrix and b in . - algebraic multiplicity
- The multiplicity of an eigenvalue as a root of the characteristic equation.
- angle
- Between nonzero vectors
**u**and**v**in and . The angle between the two directed line segments from the origin to the points**u**and**v**. Related to the scalar product by

## B

[edit | edit source]## C

[edit | edit source]- coefficients
- A constant by which a variable are multiplied, fx. are a coefficient in the following equation .
- consistent linear system
- A linear system with at least one solution.

## D

[edit | edit source]## E

[edit | edit source]- equivalent linear systems
- Linear systems with the same solution set.
- echelon form
- Also called
**row echelon form**. An echelon matrix that is row equaivalent to the given matrix. - echelon matrix
- Also called
**row echelon matrix**. A rectangular matrix that has three properties: (1) All nonzero rows are above any row of all zeros. (2) Each leading entry of a row is in a column to the right of the leading entry of the row above it. (3) All entries in a column below a leading entry are zero.

## F

[edit | edit source]## G

[edit | edit source]## H

[edit | edit source]## I

[edit | edit source]- inconsistent linear system
- A linear system with no solution.

## K

[edit | edit source]## L

[edit | edit source]- linear equation
- An equation that can be written in the form , where
*b*and the coefficients are real or complex numbers. - linear system
- A collection of one or more linear equations involving the same variables, fx. .

## M

[edit | edit source]## N

[edit | edit source]## O

[edit | edit source]## P

[edit | edit source]## Q

[edit | edit source]## R

[edit | edit source]- reduced echelon form
- Also called
**reduced row echelon form**. A reduced echelon matrix that is row equivalent to a given matrix. - reduced echelon matrix
- A rectangular matrix in
**echelon form**that has these additional properties: The leading entry in each nonzero row is 1, and each leading 1 is the only nonzero entry in its column. - reduced row echelon form
- See
**reduced echelon form**. - row echelon form
- See
**echelon form**. - row echelon matrix
- See
**echelon matrix**.

## S

[edit | edit source]- solution
- A list of numbers that makes each equation in system a true statement when the values are substituted for respectively.
- solution set
- The set of all possible solutions of a linear system. The solution set is empty when the linear system is inconsistent.
- system of linear equations
- Also called a
**linear system**, is a collection of one or more linear equations involving the same set of variables, fx. .