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AI•Mathematics

Matrices

A matrix is set of

Numbers.

A matrix is an

Rectangular Array.

A matrix is arranged in

Rows and

Columns.

Matrix Dimensions

This

Matrix has

row and

columns: C =

The

Dimension of the matrix is (

x

).

This matrix has

rows and

columns: C =

The dimension of the matrix is (

x

).

Square Matrices

A Square Matrix is a matrix with the same number of rows and columns.

Formula

An n - by - n matrix is known as a square matrix of order n.

A

Formula

2 - by - 2 matrix (Square matrix of order 2):

C =

A

Formula

4 - by - 4 matrix (Square matrix of order 4):

C =

-2

-7

-1

-5

Diagonal Matrices

A Diagonal Matrix has values on the diagonal entries, and zero on the rest: C =

Scalar Matrices

A Scalar Matrix has equal diagonal entries and zero on the rest: C =

The Identity Matrix

The

Identity Matrix has

on the diagonal and

on the rest. This is the matrix equivalent of 1. The symbol is I. I =

If you multiply any matrix with the identity matrix, the result equals the original.

The Zero Matrix

The

Zero Matrix

(Null Matrix) has only zeros. C =

Equal Matrices

Matrices are

Equal if each element correspond:

=

Negative Matrices

The

Negative of a matrix is easy to understand:

-2

-4

=

-5 -3

-7 -1

Linear Algebra in JavaScript

In linear algebra, the most simple math object is the

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Vectors

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Tensors