Addition of matrices

← Back: The transpose of a matrix

Overview: Matrices

Next: Multiplication with a vector →

Requirement for the addition of two matrices is, that they have the same number of rows and the same number of colums. So both matrices have to be an m-by-n matrix. The addition is made by adding each the components:

$\mathbf{A}+\mathbf{B}= \left[\begin{array}{cccc} a_{11} & a_{12} & \dots &a_{1n} \\ a_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1} & \dots & & a_{mn} \end{array}\right]+ \left[\begin{array}{cccc} b_{11} & b_{12} & \dots &b_{1n} \\ b_{21} &\ddots & &\vdots\\ \vdots & & & \\ b_{m1} & \dots & &b_{mn} \end{array}\right]= \left[\begin{array}{cccc} a_{11}+b_{11} & a_{12}+b_{12} & \dots &a_{1n}+b_{1n} \\ a_{21}+b_{21} &\ddots & &\vdots\\ \vdots & & & \\ a_{m1}+b_{m1} & \dots & &a_{mn}+b_{mn} \end{array}\right]$