definition of conjugate of matrix by invertible matrix
Topics
About: ring
About: matrices space
The table of contents of this article
Starting Context
- The reader knows a definition of ring of \(n \times n\) ring matrices.
Target Context
- The reader will have a definition of conjugate of matrix by invertible matrix.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Structured Description
Here is the rules of Structured Description.
Entities:
\( R\): \(\in \{\text{ the rings }\}\)
\( n\): \(\in \mathbb{N} \setminus \{0\}\)
\( M_n (R)\): \(= \text{ the ring of the } n \times n R \text{ matrices }\)
\( M\): \(\in M_n (R)\)
\( N\): \(\in \{\text{ the invertible matrices in } M_n (R)\}\)
\(*N M N^{- 1}\):
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Conditions:
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2: Note
A main reason why we take up this concept is that it appears in the proposition that for any module with any \(2\) bases of any same finite cardinality and any module endomorphism, the transition of the endomorphism matrices with respect to the change of the bases is this.
