EE 503 : Lecture 4 Fall 2020 METU

EE 503 - Statistical Signal Processing and Modeling Fall 2020 Middle East Technical University Ankara Turkey. Instructor : Prof. Cagatay Candan Lecture 4 Playlist : Lecture Contents: 0:00 - Inner Product Norm Axiom reminder 2:00 - Cauchy Schwarz Inequality proof 8:40 - Cauchy Schwarz Equality case 13:00 - angle between vectors 14:40 - Example: Cosine theorem of 2D3D Euclidean geometry 20:00 - Orthogonality of vectors aligned vectors 24:30 - Triangle inequality for the induced norm proof 27:40 - Vector spaces normed spaces inner product spaces 30:30 - Projection matrices problem statement again! 34:27 - Orthogonality conditions for the projection point projectors 41:03 - Orthogonality condition in matrix-vector form projectors 42:59 - Solving the projection point projectors 43:50 - Case of invertible Gram matrix Solving the projection point 45:30 - Projection matrix expression finally! Corrections: 11:05 x lambda_x y should be x - lambda_x y Ugur Berk S. 15:30 xy inner product should be xy x1 times y1 x2 times y2 Ada G.,

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