The definition of equivalence is:

There are invertible matrices P and Q, so that QAP=B, then matrix A is said to be equivalent to matrix B.

A similar definition is:

There is an invertible matrix p such that P (- 1) AP = B, then matrix a is similar to matrix b, (P- 1 stands for the inverse matrix of p).

Definition of contract:

There is an invertible matrix p such that (PT)AP=B, then matrix A is called a contract with matrix B, (PT stands for the transposition of p).

As can be seen from the above formula,

P (- 1) and PT are special cases of q,

Therefore, if two matrices are similar or contracted, they must be equivalent.

In other words, similar contracts are special cases of equivalence.