Embedded Files
In this course, we will be learning some basics of Linear Algebra with its application to applied engineering. Instead of proving theorems from axioms and definitions, I focus on explaining how things are actually being computed, namely, "What is happening inside NumPy and SciPy". One might argue that all we need is to simply know is how to use such packages. However, it is possible to get orders of magnitude faster speedups by using right APIs at right places. One representative example is to use LU decomposition for solving linear systems. In depth-wise, this course will not go beyond undergraduate-level linear algebra.
Speedups of using LU decomposition on solving linear systems
Syllabus
Syllabus
Week 1 - Linear equations
Course Logistics
Introduction to LaTex
How to solve a linear system
Row reduction and echelon form
Solution of linear systems via row reduction
Existence and uniqueness
Summary
Week 2 - Matrix Operations
Review of linear equations
What is a matrix
The span of a set of vectors
Matrix operations
Week 3 - LU decomposition
Review of linear equations and matrix operations
Elementary matrices
Gaussian elimination revisited
LU decomposition
Week 4 - The inverse of a matrix
Review
The inverse of a matrix
Solving systems using matrix inverse
Recipe for computing the inverse
LU decomposition vs. matrix inverse
Week 5 - Vector space
Vector space
Subspace
Span of vectors are subspaces
Week 6 - Solving linear equation
Column spaces
Null spaces
Another look at solutions to Ax = b
Week 7 - Subspace
Linear independence
Week 8 - Mid-term
Week 9 - Linear transformation
Week 10 - Orthogonal vectors
Week 11 - Least squares
Week 12 - Gram-Schmidt (QR decomposition)
Week 13 - Determinants
Week 14 - Eigenvectors and eigenvalues
Week 15- Cholesky decomposition
Week 16 - Final-term
Page updated
Google Sites
Report abuse