Statistics Dictionary

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Inverse

Suppose A is an n x n matrix. The inverse of A is another n x n matrix, denoted A-1, that satisfies the following conditions.

AA-1 = A-1A = In

where In is the identity matrix. Below, with an example, we illustrate the relationship between a matrix and its inverse.

2 1
3 4
0.8 -0.2
-0.6 0.4
    =    
0.8 -0.2
-0.6 0.4
2 1
3 4
    =    
1 0
0 1
A A-1 A-1 A I

See also:  Matrix Inverse