Matrix equivalence

The equivalence in the mathematical subfield of linear algebra is an equivalence relation on the class of matrices.

Two matrices and are by definition equivalent if there is a linear map

That is, is a view of the base with respect to and from, and is a diagram of relation to the base of and.

Equivalent statement

With the statement ' the matrices and are equivalent to the body " is equivalent to the following statement:

• There are over an invertible matrix and an invertible matrix, so that applies.

Statements about equivalent matrices

• Two regular matrices of the same type are equivalent.
• Two matrices of the same type and the same rank are equivalent.

Equivalent matrices and similar matrices

A special case of the equivalent matrices similar matrices.