Similar Matrices and Similarity Invariants | Linear Algebra

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   🛍 Check out my math fashion brand! https://mathshion.com/ 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 introduce similar matrices, similarity transformations, similarity invariants, we prove some similarity invariants, prove transitivity of similar matrices, go over how to show 2 matrices are similar given an invertible matrix P that creates the similarity transformation, and do three examples showing matrices aren't similar. #linearalgebra Proving Similarity Invariants: (coming soon) Diagonalizing a Matrix:    • Diagonalizing Matrices and Diagonalizabili...   ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits:   / wrathofmathlessons   ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● Twitter:   / wrathofmathedu   0:00 Intro 0:19 Similarity Transformations 0:49 Similarity Invariants 2:14 Proof Similar Matrices have Same Determinant 3:16 Proof Similar Matrices Share Invertibility 4:42 Definition of Similar Matrices 5:21 Symmetry of Similar Matrices 6:24 Transitivity of Similar Matrices 7:38 Showing Two Matrices are Similar 9:41 Showing Two Matrices aren't Similar 11:31 Conclusion