The relationship among similarity, congruence, equivalence and rank of matrix For example, if two matrices are equivalent, we can deduce the rank equality of these two matrices,

The relationship among similarity, congruence, equivalence and rank of matrix For example, if two matrices are equivalent, we can deduce the rank equality of these two matrices,

The rank of similar matrices is also equal,
The definition of similar matrix is: there is an invertible matrix P of order n
If p-1ap = = = B, then a and B are similar
The rank of mutually congruent matrices is also the same
The definition of the contract between matrices is that there exists an invertible matrix C of order n
Make: CTAC = = B on the main a, B contract
Both similarity and contract are equivalent