Algorithm for Matrix Multiplication

What is Matrix Multiplication in Maths?

Matrix multiplication is the mathematical operation that is performed on two matrices which when multiplied gives a singular matrix....

How to Multiply Matrices?

Suppose we have to find the multiplication of two matrices A and B where the number of columns in A is equal to the number of rows in B such that the multiplication of A and B is obtained in such a way that we multiply the first row of the first matrix with the first column of the second matrix to get the first element of the multiplied matrix....

What are the Matrix Multiplication Rules?

Note that the multiplication of any two matrices is possible only if both matrices are compatible. We can multiply two matrices if the number of columns in the 1st matrix is equal to the number of rows in the 2nd matrix, otherwise, the given matrices cannot be multiplied....

Matrix Multiplication Notation

We represent a multiplication matrix as the multiplication of two matrices A and B such that the order of A is m×p and the order of B is p×n then the order of the multiplied matrix is m×n. Then...

Matrix Multiplication Formula

Let’s take two matrices A and B of order 3×3 such that A = [aij] and B = [bij]. Then the multiplication of A and B is obtained in the image such that,...

Algorithm for Matrix Multiplication

There are various matrix multiplication algorithms that are widely used for finding matrix multiplication and some of the most common matrix multiplication algorithms are,...

Matrix Multiplication Rules

Some rules for matrix multiplication are,...

2×2 Matrix Multiplication Formula

Let us consider two matrices A and B of order “2 × 2”. Then its multiplication is achieved using the formula....

3×3 Matrix Multiplication Formula

Let us consider two matrices P and Q of order “3 × 3”. Now, the matrix multiplication formula of “3 × 3” matrices is,...

Matrix Multiplication by Scalar

A matrix can be multiplied by a scalar value, which is called scalar multiplication, and also by a matrix, which is called matrix multiplication. Scalar multiplication is the multiplication of a matrix by a scalar value. When a matrix “A = [aij]” is multiplied by a scalar value “k,” every element of the given matrix is multiplied by the scalar value. The resultant matrix is expressed as kA, where kA = k[aij] = [kaij], for all the values of i and j....

Properties of Matrix Multiplication

The following are some important properties of matrix multiplication:...

Matrix Multiplication Examples

Some examples on Matrix Multiplication are,...

Practice Problems on Matrix Multiplication

Solve the following problems:...

Conclusion – Matrix Multiplication

Matrix multiplication is a fundamental mathematical operation that involves combining information from two matrices to produce a new matrix. By following specific rules, we can efficiently multiply matrices and obtain results crucial for solving systems of equations, describing geometric transformations, analyzing data relationships, and more....

FAQs on Matrix Multiplication

Define Matrix Multiplication....