http://mathworld.wolfram.com/CongruentMatrices.html
Two square matrices 
and 
are called congruent if there exists a nonsingular matrix 
such that
 |
where 
is the transpose.
Congruent
Exactly equal in size and shape. Congruent sides or segments have the exact same length. Congruent angles have the exact same measure. For any set of congruent geometric figures, corresponding sides, angles, faces, etc. are congruent.
Note: Congruent segments, sides, and angles are often marked.
Congruent Segments Congruent Angles
All four sides of this rhombus are marked to show they are congruent to each other.
The marked angles of this isosceles triangle are congruent to each other.
原文：http://www.cnblogs.com/yuanjiangw/p/7782094.html