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| Date | Sections | Topics covered | Homework assignments |
| 1/28 | s. 1.1 | Definition of a vector space. Examples | # 1.1-1.4 |
| 1/30 | s. 1.2 | Basis, linear independence, generating (complete) sets | Click here to see the assignment |
| 2/2 | s.1.3 | Linear transformations. Matrix-vector multiplication | Click here to see the assignment (will be collected 2/4) |
| 2/4 | s. 1.4 | Composition of Linear transformations. Matrix Multiplication. | Click here to see the assignment Solutions, PDF, 57K |
| 2/6 | s. 1.5 | Invertible transformations and matrices. Isomorphisms | Click here to see the assignment Solutions, PDF, 37 K |
| 2/9 | s. 1.7, read 1.6 new version |
Applications to computer graphics | Click here to see the assignment |
| 2/11 | Ch. 2. s. 1, 2 | Many faces of linear systems. Solving linear systems by row reduction | Click here to see the assignment |
| 2/13 | Ch 2 s. 3 | What can be said from analysis of pivots. Inverting matrices | Click here to see the assignment To be collected 2/16 See solution of # 7 (PDF, 43 K) |
| 2/16 | Ch 1 s. 6, Ch 2 s. 4, 5, beginning of 6 | Dimension, subspaces. Fundamental subspaces of a matrix | Click here to see the assignment
Solutions, PDF, 68 K |
| 2/18 | Ch 2 s. 6 | Computing fundamental subspaces. Rank Theorem. | Click here to see the assignment, |
| 2/20 | Ch 2 s. 6 | Review of dimension and rank. | Click here to see the assignment, Also read s. 7 of Ch 2. |
| 2/23 |
Long weekend |
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| 2/25 | Ch 2 s 7 | Change of basis formula | Click here to see the assignment (will be collected Fri. Feb. 27) |
| 2/27 | Ch. 3 S. 1--3 | Determinants: Introduction, properties. | Click here to see the assignment |
| 3/1 | Ch 3 s 3, 5 | Determinants. Cofactor (row) expansion | Click here to see the assignment (will be collected Wed. March 3) Solutions for #6, 5 (PDF, 105K) |
| 3/3 | Ch. 3 s. 5 | Cofactor expansion, cofactor formula for the inverse, Cramer's rule | Click here to see the assignment |
| 3/5 | Ch. 3 s. 4 | Formal definition of determinant. Permutations. | Click here to see the assignment will be collected Mon. March 8. |
| 3/8 | |||
| 3/10 | Test 1 | Click here to see solutions for the test (PDF, 112 K) | Click here to see the assignment |
| 3/12 | Ch 4, s. 1, beginning of s. 2 | Eigenvalues and eigenvectors | Click here to see the assignment (will be collected Mon. March 15) |
| 3/15 | Ch. 4, s. 1,2 | Diagonalization. | Click here to see the assignment |
| 3/17 | Ch. 4, s. 1,2 | Diagonalization, bases of subspaces | Click here to see the assignment |
| 3/19 | Ch 5, s. 1 | Inner product spaces. | Click here to see the assignment (will be collected Mon. March 22) |
| 3/22 | Ch 5, s. 1, 2 | Cauchy-Schwarz inequality. Orthogonal and orthonormal basis. | Click here to see the assignment |
| 3/24 | Ch 5, s 3. | Orthogonal projection. Orthogonal complement. | Click here to see the assignment |
| 2/26 | Ch. 5 s. 3 | Gram--Schmidt orthogonalization. | Click here to see the assignment |
| 3/29 |
Spring recess |
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| 3/31 | |||
| 4/2 | |||
| 4/5 | Ch. 5 s. 4 | Least square solution. Formula for the orthogonal projection | Click here to see the assignment will be collected 4/7 solutions |
| 4/7 | Ch 5 s. 5 | Adjoint operators. Fundamental subspaces revisited. | Click here to see the assignment |
| 4/9 | Ch. 5, s. 6 | Isometries, unitary and orthogonal matrices | Click here to see the assignment |
| 4/12 | Ch. 6.s 1, 2 | Schur (upper triangular) representation of a matrix. Spectral theorem for self-adjoint (Hermitian) matrices. | Click here to see the assignment Solutions |
| 4/14 | Ch 6. s 2. | Normal operators. Spectral theorem for normal operators. | Click here to see the assignment
\(to be collected 4/16) Solutions (to selected problems) |
| 4/16 | Ch. 6 s. 3.1, 3.2 | Positive definite and positive semidefinite operators. Modulus of an operator, singular values. |
Click here to see the assignment |
| 4/19 | Review | ||
| 4/21 | Test 2 | ||
| 4/23 | Ch 6 s. 3.3, 3.4. | Singular Value decomposition. |
Click here to see the assignment |
| 4/26 | Ch. 6, s 3.3, 3.4. Read s. 4. | Singular Value Decomposition. Matrix form |
Click here to see the assignment (will be collected 4/28) |
| 4/28 | Ch. 6, s. 4 | What SVD tells us about? | Click here to see the assignment |
| 4/30 | Ch 7, s. 1, 2 | Quadratic forms. Diagonalization, orthogonal diagonalization. | Click here to see the assignment |
| 5/3 | Ch. & s 3, 4 | Silvester Criterion of Positivity | Click here to see the assignment |
| 5/5 | |||
| 5/7 | |||
| 5/10 | Review for the final | ||