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Show that similarity of matrices is an equivalence relation. That is, verify the
Chapter 4, Problem 21(choose chapter or problem)
Show that similarity of matrices is an equivalence relation. That is, verify the following.
a. Reflexivity: Any matrix is similar to itself.
b. Symmetry: For any matrices and , if is similar to , then is similar to .
c. Transitivity: For any matrices , and , if is similar to and is similar to , then is similar to .
Questions & Answers
QUESTION:
Show that similarity of matrices is an equivalence relation. That is, verify the following.
a. Reflexivity: Any matrix is similar to itself.
b. Symmetry: For any matrices and , if is similar to , then is similar to .
c. Transitivity: For any matrices , and , if is similar to and is similar to , then is similar to .
ANSWER:Step 1 of 4
It is known that, a matrix is similar to , if there exists an invertible matrix such that,
.
To show that similarity of matrices is an equivalence relation.