Why MATLAB So Fast in Matrix Multiplication?

 In simple words, we say that Since MATLAB was originally created for numerical linear algebra (matrix manipulations), it has libraries that were specifically created for matrix multiplications. The same program is run for each data element, which reduces the need for complex flow control. Additionally, because the program is run on many data elements and has a high arithmetic intensity, calculations can be used to hide memory access latency in place of big data caches.  that’s why MATLAB is so fast in matrix Multiplication.

How Fast is Matrix Multiplication?

The number of multiplications required to find a matrix’s product grows much more quickly than the number of additions. To find the product of two-by-two matrices, eight intermediate multiplications are required, whereas 64 are required to find the product of four-by-four matrices.

How does MATLAB Multiply Matrices?

Matrix multiplication is possible only if the number of columns n in U is equal to the number of rows n in V. In matrix multiplication, the elements of the first matrix’s rows are multiplied by those of the second matrix’s columns. If U is an m x n matrix and V is an n x p matrix, they could be combined to produce an m x p matrix Z.
The sum of the products of elements in the ith row of the first matrix and the corresponding element in the jth column of the second matrix yields each element in the (i, j)th position of the final matrix Z. The * operator is used in MATLAB to perform matrix multiplication.

Example 1:

Matlab

a = [ 9 8 7; 5 6 7; 1 2 3]
b = [ 3 4 7; 6 4 3; -2 3 4 ]
prod = a * b

Output:

The file displays the following outcome when you run 

Fastest Algorithm for Multiplying Matrices:

The Strassen algorithm is a matrix multiplication algorithm used in linear algebra. It is named after Volker Strassen.Although the naive algorithm is frequently superior for smaller matrices, it is faster than the standard matrix multiplication algorithm for large matrices and has a lower asymptotic complexity. it reduces the total number of operations, Strassen’s matrix multiplication (MM) has advantages over any (highly tuned) MM implementation. By substituting matrix additions (MAs) for the computationally expensive MMs, Strassen was able to reduce the number of operations.

Is matrix multiplication faster than for loops in MATLAB? So due to the libraries, you are using. A straightforward for loop uses the Python interpreter, which is incredibly slow. It’s more likely that a good matrix library you’re using is just a Python wrapper for the much faster C or C++ math libraries.