c7s2 - 7.2 Matrix Representations and Similarity 1 Chapter...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7.2 Matrix Representations and Similarity 1 Chapter 7. Change of Basis 7.2 Matrix Representations and Similarity Theorem 7.1. Similarity of Matrix Representations of T . Let T be a linear transformation of a Fnite-dimensional vector space V into itself, and let B and B be ordered bases of V . Let R B and R B be the matrix representations of T relative to B and B , respectively. Then R B = C 1 R B C where C = C B ,B is the change-of-coordinates matrix from B to B . Hence, R B and R B are similar matrices. Example. Page 406 number 2. Theorem. SigniFcance of the Similarity Relationship for Ma-trices. Two n n matrices are similar if and only if they are matrix represen-tations of the same linear transformation T relative to suitable ordered bases. 7.2 Matrix Representations and Similarity 2 Proof. Theorem 7.1 shows that matrix representations of the same trans-formation relative to diFerent bases are similar. Now for the converse. Let A be an n n matrix representing transformation...
View Full Document

Page1 / 4

c7s2 - 7.2 Matrix Representations and Similarity 1 Chapter...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online