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Description

Summer 2015

MATH 2940

week 1 notes

1/27/16: Introduction 1/29/16: Systems of Linear Equations

Introduction Systems of Linear Equations

Introduction System of Linear Equations

Row Reduction Vector Equations Ax=b

These are the notes for the second week of Math 2940, Linear Algebra for Engineers

Solution sets Linear Independence Linear Transformations

Matrix of a Linear Transformation Matrix Operations

Covering textbook chapters 1.1 to 1.9 (excluding 1.6)

Matrix Inverse

Vector Spaces Null and column spaces Linear independence; bases

Change of Basis Difference Equations Determinants

Determinants Eigenvalues & Eigenvectors Characteristic Equation

Diagonalization Eigenvectors & linear transformations Complex eigenvalues

Discrete Dynamical Systems Markov Chains Differential Equations

Covering roughly textbook chapters 2.1 to 5.6 (chapters go by order introduced in lecture)

Inner Product Orthogonal Sets

Orthogonal Projections NOT INCLUDED (was out of town that day) Gram-Schmidt Least-square Method

Diagonalization of Symmetric Matrices Quadratic Forms Signular-value Decomposition

Singular-Value Decomposition Continued

Covering textbook chapters 5.7 to 7.4 (as on the course syllabus)