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Matrix Size & Validation
Vector Algebra What is Vector? Vector Norm Unit Vector Vector Addition Vector Subtraction Vector Scalar Multiple Vector Multiplication Vector Inner Product Vector Outer Product Vector Cross Product Vector Triple Cross Product Vector Triple Dot Product Scalar Triple Product Orthogonal & Orthonormal Vector Cos Angle of Vectors Scalar and Vector Projection Matrix Algebra What is a matrix? Special Matrices Matrix One Null Matrix Matrix Diagonal Is Diagonal Matrix? Identity Matrix Matrix Determinant Matrix Sum Matrix Trace Matrix Basic Operation Is Equal Matrix? Matrix Transpose Matrix Addition Matrix Subtraction Matrix Multiplication Matrix Scalar Multiple Hadamard Product Horizontal Concatenation Vertical Concatenation Elementary Row Operations Matrix RREF Finding inverse using RREF (Gauss-Jordan) Finding Matrix Rank using RREF Matrix Inverse Is Singular Matrix? Linear Transformation Matrix Generalized Inverse Solving System of Linear Equations Linear combination, Span & Basis Vector Linearly Dependent & Linearly Independent Change of basis Matrix Rank Matrix Range Matrix Nullity & Null Space Eigen System Matrix Eigen Value & Eigen Vector Symmetric Matrix Matrix Eigen Value & Eigen Vector for Symmetric Matrix Similarity Transformation and Matrix Diagonalization Matrix Power Orthogonal Matrix Spectral Decomposition Singular Value Decomposition Resources on Linear Algebra |
Matrix Multiplication One of the most important matrix operations is matrix multiplication or matrix product. The multiplication of two matrices Example
Example The interactive program below shows you the result of matrix multiplication. Your input must be two matrices, one with size m by n and the other one with size n by k. Random Example will generate random matrices at the right size. Try to input your own matrices to gain more understanding about matrix product. PropertiesSome important properties of matrix multiplication are
See also: matrix power, matrix inverse, vector inner product, Matrix element-wise product Rate this tutorial or give your comments about this tutorial Preferable reference for this tutorial is Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\ tutorial\LinearAlgebra\ |
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and 
is a matrix 
whose element 
consists of the vector inner product of the 
row of matrix 
and the
column of matrix
, that is
. Matrix multiplication can be done only when the number of columns of 
is equal to the number of rows of
.
is 
by
and the size of matrix 
is 
by
, then the result of matrix multiplication is a matrix size 
by
, or in short
.
, 
, 
. This is very different from multiplication of two numbers. 
. 
and 
. 
. In general, the transpose of the matrix products can be extended to several matrices 
