Orthogonality

Overview

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Explore the fundamental concepts of orthogonality in linear algebra and its applications in this comprehensive 3.5-hour course. Delve into orthogonal sets, orthogonal projections, and master the Cauchy-Schwarz inequality through detailed proofs. Learn the Gram-Schmidt process, understand least squares approximation, and discover QR decomposition. Apply these concepts to linear regression and inner product spaces. Investigate Legendre polynomials and gain insights into Fourier series, including cosine and sine series expansions. Enhance your mathematical toolkit with these essential techniques used in various fields of science and engineering.

Syllabus

Orthogonal sets.
Orthogonal Projections.
Cauchy Schwarz Proof.
Quick Cauchy Schwarz Proof.
Gram Schmidt Process.
Least Squares.
QR decomposition.
Linear regression.
Inner Product Spaces.
Legendre polynomials.
Fourier series.
Fourier cosine and sine series.