Suppose T : V &#x2192;<!-- \rightarrow --> V is the identity transformation. If B

tripes3h

tripes3h

Answered question

2022-07-07

Suppose T : V V is the identity transformation.
If B is a basis of V, then the matrix representation of [ T ] B B = [ I n ].
Let's say C is also a basis of V, then it is clear that
[ T ] C B [ I n ]
However, I was taught that matrices representing the same linear transformation in different bases are similar, and the only matrix similar to I n is I n . Thus, [ T ] C B and [ T ] B B are not similar.
Can anyone clear what seems to be a contradiction?

Answer & Explanation

Isla Klein

Isla Klein

Beginner2022-07-08Added 12 answers

What the statement “matrices representing the same linear transformation in different bases are similar” means is that if B and C are bases, then [ T ] B B and [ T ] C C are similar.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?