Linear Algebra

I. Course Overview: MIT OCW – Prof. Gilbert Strang

Linear algebra: branch of mathematics studying for linear equation system and matrix


II. Course Objective:

A. Systems of linear equation

B. Row reduction and echelon form

C. Matrix operation, including inverse

D. Block matrix

E. Linear Dependence and Independence

F. Subspace and bases and dimension

G. Orthogonal bases and Orthogonal projections

H. Gram-Schmidt process

I. Linear model and Lease square problem

J. Determinant

K. Cramer’s Rule

L. Eigenvalue and Eigenvector

M. Diagonalization

O. Symmetric Matrix

P. Positive definite matrix

Q. Similar matrix

R. Linear transformation

S. Singular Value Decomposition(SVD)


III. Prerequisite:

A. 18.02 Multi Variable Calculus


IV. Text Book:

Strang, Gilbert. Introduction to Linear Algebra. 5th ed


V. Plan:

∗ MIT students spend 150 hours for course, more than half for class and assignment