Gram-Schmidt Orthogonalization (Proof and Example) | 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 the Gram-Schmidt process for obtaining an orthonormal basis for an inner product space from an arbitrary basis. We begin by proving such a basis always exists, and this proof essentially is the Gram-Schmidt process. We then review the process necessary to construct an orthogonal basis and an orthonormal basis, and finish with a full example of carrying out the Gram Schmidt process on a set of basis vectors for R^3. #linearalgebra ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Follow Wrath of Math on... ● Instagram:   / wrathofmathedu   ● X:   / wrathofmathedu   0:00 Intro 0:31 There is Always an Orthonormal Basis 1:03 Proof 8:57 Gram-Schmidt Process 9:51 Gram-Schmidt Process Worked Out Example 14:34 Conclusion