S2 Math Exam Review - Matrices

Matrix

Matrix

A rectangular arrangement of numbers into rows and columns

Dimensions

The number of rows and columns of the matrix, in that order

Element

Any value entered into a matrix

Augmented matrix

A matrix which represents a system of equations

Scalars

Real numbers (in relation to matrices)

Scalar multiplication

Refers to the product of a real number and a matrix

Additive Commutative Property

For the given two matrices, matrix A and matrix B of the same order, then A + B = B + A

Additive Associative Property

For any three matrices, A , B, C of the same order m x n, we have A + (B + C) = (A + B) + C

Additive Identity

A + 0 = 0 + A = A

Additive Inverse

A + (-A) = (-A) + A = 0 

Multiplication Associative Property

For any three matrices A, B, C following the matrix multiplication conditions, we have (AB)C = A(BC).

Multiplication Distributive Property

For any three matrices A, B, C following the matrix multiplication conditions, we have A(B + C) = AB + AC.

Multiplicative Property

For a square matrix A, having the order m × n, and an identity matrix I of the same order we have AI = IA = A.

Dot Product

The result of multiplying the n-tuples of two matrices together.

N-tuple

An ordered set of numbers fund in a matrix. This is typically written with letters with a subscript denoting which row/column it represents.

Determinant (absolute value)

A scalar value that is a certain function of the entires of a square matrix.

Adjacency Matrix

A matrix used to represent graphs which visualize the relationships between multiple values.

Inverse

A reciprocal of a matrix’s values; the reciprocal of the determinant multiplied by its adjoint (swap top left and bottom right, add negative sign to top right and bottom left).

Multiplicative Inverse

A A^-1 = A^-1 A = I

Multiplicative Identity

The product of any n × n matrix ‍and ‍the identity matrix is always ‍equal to the n x n matrix, regardless of the order in which the multiplication was performed. A I = I A = A

Identity Matrix

A matrix of order n x n such that each main diagonal element is equal to 1, and the remaining elements of the matrix are equal to 0.