ECE551

Evolving lecture-by-lecture topics

• Lecture 1 (Aug. 27th, 2024): Fields; Vector spaces; Linear operators and matrix representation (book Chapter 1).
• Lecture 2 (Aug. 29th, 2024): Matrices (adjoint, linear-operator perspective); Vector-vector multiplication (inner product and outer product) (book Chapter 2).
• Lecture 3 (Sept. 3rd, 2024): Matrix-matrix multiplication; Invertibility; Orthogonality; Orthogonal/Unitary matrices (book Chapter 2)
• Lecture 4 (Sept. 6th, 2024): Determinant; Eigenvalues; Eigenvectors (book Chapter 2 and 3)
• Lecture 5 (Sept. 10th, 2024): Unitary eigendecomposition; Normal matrices; SVD (definition) (book Chapter 3)
• Lecture 6 (Sept. 12th, 2024): Relationships between eigendecomposition and SVD; non-uniqueness of SVD (book Chapter 3)
• Lecture 7 (Sept. 17th, 2024): Subspaces; Linear Independency; Bases; Dimension (book Chapter 4)
• Lecture 8 (Sept. 19th, 2024): Sum of subspaces; Range; Rank; Nullspace (book Chapter 4)
• Lecture 9 (Sept. 24th, 2024): Decomposition Theorem; Nullity + rank thm.; Four fundamental subspaces; Anatomy of SVD (book Chapter 4)
• Lecture 10 (Sept. 26th, 2024): Projection onto a subset; Signal classification by nearest subset; Convex sets (book Chapter 4)
• Lecture 11 (Oct. 1st, 2024): Convex functions; Linear least-squares estimation; LLS and SVD; Moore-Penrose pseudoinverse (book Chapter 4-5)
• Lecture 12 (Oct. 3rd, 2024): Pseudoinverse and SVD; LLS using peseudoinverse; Minimum-norm LLS solution via pseudoinverse (book Chapter 5)
• Lecture 13 (Oct. 8th, 2024): Condition number; Tikhonov regularization; Projection matrices (book Chapter 5)
• Lecture 14 (Oct. 10th, 2024): Orthogonal projection matrices; Projection onto a subspace (revisited); Vector norms (book Chapter 5-6)
• Lecture 15 (Oct. 17th, 2024): Unitarily invariant vector norms; Inner products; Cauchy-Schwarz inequality; Matrix norms (book Chapter 6)
• Lecture 16 (Oct. 22nd, 2024): Induced matrix norms; Matrix inner product inequalities; Singular values inequalities; Spectral radius (book Chapter 6)
• Lecture 17 (Oct. 24th, 2024): Procuste Analysis (book Chapter 6)
• Lecture 18 (Oct. 29th, 2024): Low-rank approximation via Frobenius norm; Eckart-Young-Mirsky thm: Non-uniqueness of LR approx. (book Chapter 7)
• Lecture 19 (Oct. 31st, 2024): Multidimensional scaling (book Chapter 7)
• Lecture 20 (Nov. 05th, 2024): Proximal Operators; Soft/hard thresholding; General unitarily invariant formulation (low-rank approximation) (book Chapter 7)
• Lecture 21 (Nov. 07th, 2024): Rank selection; SURE estimator; OptShrink (book Chapter 7)
• Lecture 22 (Nov. 12th, 2024): Companion matrices; Vandermonde matrices; Circulant matrices and the DFT (book Chapter 8)
• Lecture 23 (Nov. 14th, 2024): Toeplitz matrices; Power Iieration: Gersgorin disks (book Chapter 8)
• Lecture 24 (Nov. 14th, 2024): Square nonnegative matrices; Positive matrices; Primitive matrices; Irreducible matrices (book Chapter 8)