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Table of contents

What is matrix multiplication?
How to multiply matrices?
Different types of matrices

What is matrix multiplication?

Matrix multiplication is a linear algebra operation that produces a multi-dimensional structure by taking two identical matrices and dividing them by the number of columns. The resulting product, which is referred to as the matrix product, has the number of columns of the second matrix and the number of rows of the first.
Matrix multiplication

How to multiply matrices?

There are two ways to multiply a given matrix. The first is to multiply it with a scalar, and the second way is to multiply it with another matrix.
Scalar multiplication is a very simple operation. It takes the scalar and multiplies it to each entry in the matrix.
On the second method, the dot product is used to multiply two matrices and the rows and columns are treated as vectors.
How to multiply matrices

Different types of matrices

Here you will see the categorization of matrices based on their size, or in mathematical terms, categorization by dimension. Dimension refers to the size of the matrix which is written as "rows x columns".

1) Row and column matrix

These are matrices with only one row or column, hence the name.
example of a row matrix
Example of a row matrix
example of a column matrix
Example of a column matrix

2) Rectangular & square matrix

If a matrix does not have an equal number of rows and columns, it is called a rectangular matrix. On the other hand, if the matrix has an equal number of rows and columns, it is called a square matrix.
example of a rectangular matrix
Example of a rectangular matrix
example of a square matrix
Example of a square matrix

3) Singular & non-singular matrix

A singular matrix is a square matrix whose determinant is 0, and if the determinant is not equal to 0, the matrix is called non-singular.
example of a singular matrix
Example of a singular matrix
example of a non-singular matrix
Example of a non-singular matrix

The next three matrices are all "Constant Matrices". These are so that all the elements are constants for any given dimension/size of the matrix.

4) Identity matrix

An identity matrix is also a square diagonal matrix. In this matrix, all the entries on the main diagonal are equal to 1, and the rest of the elements are 0.
example of an identity matrix
Example of an identity matrix

5) Matrix of ones

If all elements of a matrix are equal to 1, then this matrix is called a matrix of ones, as the name indicates.
example of a matrix of ones
Matrix of ones

6) Zero matrix

If all the elements of a matrix are 0, then the matrix in question is a zero matrix.
example of a zero matrix
Zero matrix

7) Diagonal matrix and scalar matrix

A diagonal matrix is a square matrix in which all the elements are 0 except for those elements that are in the diagonal.
example of a diagonal matrix
Example of a diagonal matrix
On the other hand, a scalar matrix is a special type of square diagonal matrix, where all the diagonal elements are equal.
example of a scalar matrix
Example of a scalar matrix

8)Upper & lower triangular matrix

An upper triangular matrix is a square matrix in which all the elements below the diagonal elements are 0.
example of an upper triangular matrix
Example of an upper triangular matrix
On the other hand, a lower triangular matrix is a square matrix in which all the elements above the diagonal elements are 0.
example of a lower triangular matrix
Example of a lower triangular matrix

9) Symmetric and skew-symmetric matrix

An asymmetric matrix is a square matrix that is equal to its transpose matrix. If the transpose of the matrix is equal to the negativized matrix, then the matrix is skew-symmetric.
example of a symmetric matrix
Example of a symmetric matrix
inverse of the symmetric matrix
The inverse of the symmetric matrix
example of a skew-symmetric matrix
Example of a skew-symmetric matrix
inverse of the skew-symmetric matrix
The inverse of the skew-symmetric matrix

10) Boolean matrix

A boolean matrix is a matrix where its elements are either 1 or 0.
example of a boolean matrix
Example of a boolean matrix

11) Stochastic matrices

A square matrix is considered to be stochastic if all the elements are non-negative and the sum of the entries in each column is 1.
example of a stochastic matrix
Example of a stochastic matrix

12) Orthogonal matrix

A square matrix is considered orthogonal if the multiplication of the matrix and its transpose is 1.
example of an orthogonal matrix
Example of an orthogonal matrix
Types of matrices

John Cruz
Article author
John Cruz
John is a PhD student with a passion to mathematics and education. In his freetime John likes to go hiking and bicycling.

Matrix Multiply Calculator English
Published: Sat Nov 06 2021
In category Mathematical calculators
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