Matrix Multiplication
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Problem Description
Matrix multiplication or multiplication of matrices is one of the operations that can be performed on matrices in linear algebra. Multiplication of matrix A with matrix B is possible when both the given matrices, A and B are compatible. Matrix multiplication is a binary operation, that gives a matrix from two given matrices.
Matrix multiplication was first introduced in 1812 by French mathematician Jacques Philippe Marie Binet, in order to represent linear maps using matrices. Let us understand the rule for multiplication of matrices and matrix multiplication formula in detail in the following sections.
Bounds Chart
Step Chart
Improvement Table
Complexity Classes  Algorithm Paper Links  Lower Bounds Paper Links 

Exp/Factorial  
Polynomial > 3  
Cubic  [ Naive algorithm (1940)]
Strassen's algorithm (1969) (1969) Coppersmith–Winograd algorithm (1981) [ Strassen's algorithm (1986) (1986)] 

Quadratic  
nlogn  
Linear  
logn 