m
 
Line 10: Line 10:
 
To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar:
 
To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar:
  
$A = \begin{bmatrix}
+
<math>A = \begin{bmatrix}
 
a_{11} & a_{12} & \cdots & a_{1n}\\  
 
a_{11} & a_{12} & \cdots & a_{1n}\\  
 
a_{21} & a_{22} & \cdots & a_{2n}\\  
 
a_{21} & a_{22} & \cdots & a_{2n}\\  
 
\vdots & \vdots &  \ddots & \vdots \\  
 
\vdots & \vdots &  \ddots & \vdots \\  
 
a_{m1} & a_{m2} & \cdots & a_{mn}
 
a_{m1} & a_{m2} & \cdots & a_{mn}
\end{bmatrix}$, then
+
\end{bmatrix}
$c \cdot A \begin{bmatrix}
+
</math>, then
 +
<math>c \cdot A \begin{bmatrix}
 
c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot  a_{1n}\\  
 
c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot  a_{1n}\\  
 
c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot  a_{2n}\\  
 
c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot  a_{2n}\\  
 
  \vdots & \vdots &  \ddots & \vdots  \\  
 
  \vdots & \vdots &  \ddots & \vdots  \\  
 
c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot  a_{mn}
 
c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot  a_{mn}
\end{bmatrix}$
+
\end{bmatrix}</math>
  
  

Latest revision as of 23:27, 22 June 2017

Matrix Multiplication

A Matrix can be multiplied


Scalar Multiplication

To multiply a matrix on scalar, multiply each element $a_{ij}$ of the matrix on this scalar:

[math]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} [/math], then [math]c \cdot A \begin{bmatrix} c \cdot a_{11} & c \cdot a_{12} & \cdots & c \cdot a_{1n}\\ c \cdot a_{21} & c \cdot a_{22} & \cdots & c \cdot a_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ c \cdot a_{m1} & c \cdot a_{m2} & \cdots & c \cdot a_{mn} \end{bmatrix}[/math]


Sources