Linear Algebra 6.4 Transition Matrices and Similarity
Автор: Kimberly Brehm
Загружено: 2026-02-24
Просмотров: 105
Описание:
In this video, we explore transition matrices, change of basis, and similar matrices—core ideas that connect linear transformations to different coordinate systems. You’ll learn how to:
Find the matrix of a linear transformation relative to a new basis
Build change‑of‑basis matrices P and P^{-1}
Compute a new matrix representation using A'=P^{-1}AP
Understand what it means for two matrices to be similar
See worked examples
Video Chapters:
00:00 — Intro
00:07 — Transition matrices: A, A', P, and P^{-1}
02:27 — Example 1: Finding A' using A'=P^{-1}AP
03:52 — Example 2: Converting between two non‑standard bases
06:10 — Example 3: On your own
07:34 — Definition of similar matrices
09:00 - Example 4: Using a given P to compute a similar matrix
10:21 — Example 5: 3×3 similarity transformation
11:28 — Up Next
Textbook: Elementary Linear Algebra 8e, Ron Larson
Slide Decks: https://bellevueuniversity-my.sharepo...
Playlist: • Linear Algebra (Full Course)
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