Matrix Multiplication

Matrix Multiplication

The calculator computes the product of two matrices. Some theory on the topic is placed below the calculator.

PLANETCALC, Matrix Multiplication

Matrix Multiplication

Digits after the decimal point: 2
Result
 

For those who forgot, The product C of two matrices A(m \times n) and B(n \times q) is defined as:
A = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix},\;\;\; B = \begin{bmatrix} b_{11} & b_{12} & \cdots & b_{1q} \\ b_{21} & b_{22} & \cdots & b_{2q} \\ \vdots & \vdots & \ddots & \vdots \\ b_{n1} & b_{n2} & \cdots & b_{nq} \end{bmatrix}.

C = A \times B = \begin{bmatrix} c_{11} & c_{12} & \cdots & c_{1q} \\ c_{21} & c_{22} & \cdots & c_{2q} \\ \vdots & \vdots & \ddots & \vdots \\ c_{m1} & c_{m2} & \cdots & c_{mq} \end{bmatrix},

where:
c_{i,j} = \sum_{r=1}^n a_{i,r}b_{r,j} \;\;\; \left(i=1, 2, \ldots m;\;j=1, 2, \ldots q \right).

Therefore, for matrix multiplication to be defined, the dimensions of the matrices must satisfy
(n \times m)(m \times p)=(n \times p)

Note that matrix multiplication is not commutative (unless A and B are diagonal and of the same dimension).

URL copied to clipboard
PLANETCALC, Matrix Multiplication

Comments