Similar Linear Operators with Different Bases | Linear Algebra

🛍 Check out the coolest math clothes in the world! https://mathshion.com/ ❤️ Support the production of this course by joining Wrath of Math to access all my Linear Algebra videos plus lecture notes at the premium tier!    / @wrathofmath   Linear Algebra course:    • Linear Algebra   Linear Algebra exercises:    • Linear Algebra Exercises   Get the textbook for this course! https://amzn.to/45KYgmA Business Inquiries: [email protected] We discuss matrices for linear operators with respect to different bases. We'll study the relationship that exists between transformation matrices for the same linear operator, prove a theorem establishing an equivalence between identity operators and transition matrices, and a theorem connecting linear operators with respect to different bases. We finish by discussing similarity invariants, and the determinant and eigenvalues of a linear operator. #linearalgebra Gaussian Elimination:    • A Guide to Gaussian Elimination Method (an...   Transition Matrices:    • How to Find Transition Matrix Between Base...   Linear Transformations:    • General Linear Transformations on Vector S...   ★DONATE★ ◆ Support Wrath of Math on Patreon:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● TikTok:   / wrathofmathedu   ● X: https://x.com/wrathofmathedu 0:00 Intro 1:20 A Simple Transformation Matrix 4:53 Transition Matrices 7:12 Transition Matrices and Identity Operators 10:20 Connecting Transformation Matrices with Different Bases 16:22 Example of Similar Operators 18:47 Similarity Invariants 20:33 Determinant of a Linear Operator 21:30 Eigenvalues of a Linear Operator 23:02 Conclusion