RedCrab Math Tutorial

Matrix Definition

A matrix (plural matrices) is a group of mathematical objects in a rectangular arrangement, like the figure below.

With these matrices can be calculated in certain ways. For example, by adding or multiplying matrices. This article gives an overview of the different types of matrices.
definition of a matrix
  • The dimensions of the matrix are called p and q

  • In the term aij, i denotes the index of the line and j the index of the column


Square Matrix

A square matrix is called a matrices that split an equal number and have rows.

square matrix example


Diagonal Matrix

A diagonal matrix is square and all non-diagonal elements are zero.
diagonal matrix example

Identity Matrix or Unit Matrix

An identity matrix or unit matrix is a quadratic matrix whose main diagonal is filled with ones. All other elements are null.
identity matrix or unit matrix example

Zero Matrix or Null Matrix

A zero matrix or null matrix is a matrix where all elements are zero. Written as 0mn.
zero matrix examplenull matrix example0-matrix

Upper Triangular Matrix

An upper triangular matrix has all elements below the diagonal element equal to zero.
upper triangle matrix example

Lower Triangular Matrix

A lower triangular matrix has all elements above the diagonal element equal to zero.
lower triangular matrix example
Matrices of one column or row are called vectors. Matrices with one column are column vectors. Likewise, matrices with one row are row vectors.
Matrices or vectors may be transpose. That means that the 1st row becomes the 1st column, the 2nd row the 2nd column, etc. The symbol to indicate a transpose is usually a capital superscript T.
matrix transposetransposed matrix

Matrices Definition
Matrices Calculation
Matrices & Simultaneous Equations
Matrices Determinants
Row Operations of Matrices
Matrices and Geometry, Reflection
Matrices and Geometry, Rotation

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