Linear Algebra @ SUNYIT (mat340/edmond), inspired by Prof. Strang's Linear Algebra
18.06 OCW lectures.
We solve Ax = b. Applications: computational science, linear dynamical systems, robotics and machine learning.
Tasks and Homework:
8/30:
The Geometry of Linear Equations - row picture, column picture, matrix form.
Applications in Linear Dynamical Systems - can skip to 15:15; the beginning is funny but content free; look for your favorite application
Ch. 8 Applications - skim and look for your favorite application
Ch 1. Intro to vectors - work through
1.1 Vectors and Linear Combinations page8/1-13 (as always, those with answers at the back)
1.2 Lengths and Dot Products p19/1-13
1.3 Matrices p29/1-4
2.1 Vectors and Linear Equations p40/1-8
9/1: 2.1 continued p40 / 12-30 2.2 The idea p51 / 1-30
2.3 Elimination using matrices p63 / 1-25 2.4 Algebra p75 / 1-30 More Applications in LDS 9/6: 2.5 Inverse Matrices p89 / 1-30
2.6 Elimination = LU Factorization p102 / 1-20
9/8:
2.7 Transposes, Permutations, PA=LU p115 / 1-20
3.1 Vector Spaces p127 / 1-30
LDS apps - up to about 45:00; optionally, watch the rest to get a preview and a feel for applications of Ch.3
9/13:
Review for Test 1
9/15:
Test 1
9/20:
9/27:
3.5 Independence, Basis and Dimension p178 / 1-34
N(A) and C(A) - intuition and applications (45:00 -> end) - a bit advanced, so watch, sit back and relax; just get a feel for it and remember that this is actually very meaningful and useful.
9/29:
Watch Independence, Basis and Dimension for the second time and try to catch a small error
3.6 The cover of the book: The Four Fundamental Subspaces p190 / 1-20
10/4:
Skim Ch. 8 Applications, in particular 8.1 and 8.2.
8.2 Application: Graphs and Networks p428 / 1-11
10/6:
Review for Applications (45:25 -> end)
Nullspace and column space in applications. (start -> 47:00)
10/11: Mini break: Enjoy!!!
10/13:
4.1 Orthogonality of the Four Subspaces p202 / 1-25
4.2 Projections p214 / 1-20
10/18:
Great application:
4.3 Least Squares p226 / 1-20 Application: Robotics
Review for Test 2
10/20:
Test 2
10/25:
4.4 Orthogonal Matrices and Gram-Schmidt p239 / 1-20
A more applied look at Orthogonality (from 47:00 on), Fourier Series, Gram-Schmidt and QR and Least Squares10/27: 5.1 Properties of Determinants p251 / 1-32 5.2 Determinant Formulas and Cofactors p263 / 1-20 Optional: Least Squares Applications - may give you ideas for a project 11/1: 5.3 Cramer's Rule and Volumes p279 / 1-20 6.1 Eigenvalues and Eigenvectors p293 / 1-30 11/3: Catch up
Optional: Least norm solution (till 44:00)
11/8: 6.2 Diagonalizing a Matrix p307 / 1-20 6.3 Applications to Differential Equations p325 / 1-25 Same topic, in engineering: Autonomous Linear Dynamical Systems (from 44:00 on) 11/17: Test 3 11/29: 6.7 Singular Value Decomposition (SVD) p371 / 1-10 12/01: 7.1 Linear Transformations p380 / 1-25 Optional: Change of basis; Image Compression 12/06: 7.3 Pseudoinverse p406 / 1-10 Optional: Ch. 8. Applications skim
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