Matrix addition

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, matrix addition is the operation of adding two <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrices</a> by adding the corresponding entries together. 
For a <a href="/facts/Vector_space/M1pxMLx2">vector</a>, 
 
 
 
 
 
 
 v
 →
 
 
 
 
 
 
 {\displaystyle {\vec {v}}\!}
 
, adding two matrices would have the geometric effect of applying each matrix transformation separately onto 
 
 
 
 
 
 
 v
 →
 
 
 
 
 
 
 {\displaystyle {\vec {v}}\!}
 
, then adding the transformed vectors.

A
        
        
          
            
              v
              →
            
          
        
        +
        
          B
        
        
          
            
              v
              →
            
          
        
        =
        (
        
          A
        
        +
        
          B
        
        )
        
          
            
              v
              →
            
          
        
        
      
    
    {\displaystyle \mathbf {A} {\vec {v}}+\mathbf {B} {\vec {v}}=(\mathbf {A} +\mathbf {B} ){\vec {v}}\!}

However, there are other operations that could also be considered <a href="/facts/Addition/apFWJBFB">addition</a> for matrices, such as the <a href="/facts/Direct_sum/x3ljVsP6">direct sum</a> and the <a href="/facts/Kronecker_sum/gABGx6I6">Kronecker sum</a>.

Matrix addition open-in-new

Matrix addition