Orthogonal Diagonalization Explained | Linear Algebra

🛍 Check out the coolest math clothes in the world! 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 orthogonal similarity and orthogonal diagonalization. We'll prove the Fundamental Theorem of Symmetric Matrices establishing the equivalence between symmetric matrices and orthogonal diagonalizability. We'll go over how to orthogonally diagonalize a matrix step by step by finding the eigenvectors and using the Gram-Schmidt process, and complete an example of the orthogonal diagonalization of a 3x3 matrix. #linearalgebra ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● X:   / wrathofmathedu   0:00 Intro 0:45 Orthogonal Similarity 1:33 Symmetry of Orthogonal Similarity 2:33 Orthogonally Diagonalizable 3:43 Eigenvectors from Distinct Eigenspaces are Orthogonal 5:50 Fundamental Theorem of Symmetric Matrices 11:37 Step by Step Orthogonal Diagonalization 12:39 Orthogonal Diagonalization of a 3x3 Matrix 15:53 Conclusion