MATH 415 Lecture 21
Orthogonal projection onto a subspace
Wednesday 9 March 2016
Midterm 2: Thursday, March 17 from 7:00 - 8:15pm, in Foellinger Auditorium
Conflict exams: Friday, March 18 at 9 and 11am
Email your TA about conflicts by this Thursday, M
Review
Application: fitting data
Review
Gram-Schmidt
Math 415 - Lecture 25
Multiple linear regression, Gram Schmidt and Orthogonal
matrices
Wednesday July 13th 2016
Review
Application: fitting data
Textbook reading: Chapters 3.3,3.4
Review
Gram-Schmidt
Re
Review
Quadratic forms
Math 415 - Lecture 35
Quadratic forms
Tuesday July 26th 2016
Review
Quadratic forms
Math 415 - Lecture 35
Quadratic forms
Tuesday July 26th 2016
Review
Quadratic forms
Textbook reading: Chapter 6.2
Review
Quadratic forms
Textbook re
Linear transformation revisited
Data compression
Math 415 - Lecture 28
Change of base, Image Compression
Monday July 18th 2016
Linear transformation revisited
Textbook reading: Notes by Strang
Data compression
Linear transformation revisited
Textbook read
Review Directions and Equations A new perspective on Ax = b Application: Directed graphs Summary/Outlook
Math 415 - Lecture 21
Networks and linear algebra
Thursday July 7th 2016
Practice p
Review Directions and Equations A new perspective on Ax = b Applic
Review
Orthogonal projection on subspaces
Math 415 - Lecture 23
Projections on subspaces
Monday July 11th 2016
Practice problems
Review
Orthogonal projection on subspaces
Textbook reading: Chapter 3.2, 3.3, 3.4
Practice problems
Review
Orthogonal projecti
Review Linear Transformations Important Geometric Examples Representing linear maps by matrices Nonstandard Bases Additio
Math 415 - Lecture 16
Linear Transformations
Thursday June 30th 2016
Review Linear Transformations Important Geometric Examples Repre
Review
The row and column picture
Math 415 - Lecture 4
Linear Combinations and Matrix operations
Thursday June 16 2016
Matrix operations
Review
The row and column picture
Textbook: Chapter 1.3, 1.4
Matrix operations
Review
The row and column picture
Matri
Review Page rank (or: the 25000000000 $ eigenvector) Eigenbasis? Complex numbers review Back to eigenvectors Practice prob
Math 415 - Lecture 32
Complex numbers and eigenvectors
Thursday July 21st 2016
Review Page rank (or: the 25000000000 $ eigenvector)
Review
An application in wireless communication
Linear transformation revisited
Math 415 - Lecture 27
An application of QR-decomposition, Change of basis
Thursday July 14th 2016
Change of basis
Review
An application in wireless communication
Linear transf
MATH 415 Lecture 19
Networks and linear algebra
Friday, 4 March, 2015
Textbook reading: Chapter 2.5.
Suggested practice exercises: Chapter 2.5: 1, 2, 6.
Strang lecture: Lecture 12: Graphs, Networks, Incidence Matrices
1
Directed graphs
1.1
Set up
We are g
Animation Demo of Normal Approximation of Binomial
Distribution
JC Wang
October 9, 2014
Do not print this page!
Binomial Distribution
binomial(n, p) N (mean = np, SD =
npq), q = 1 p, for sufficiently large n.
With continuity correction,
binomial(n, p) 0.5
Determinants
A bad way to compute determinants, Cofactor expansion
Math 415 - Lecture 29
Determinants
Tuesday July 19th 2016
Practice Problems
Determinants
A bad way to compute determinants, Cofactor expansion
Textbook reading: Chapters 4.2, 4.3
Practice
Review
2nd derivative test
Constrained optimization
Math 415 - Lecture 36
Minima, maxima and saddle points, Constrained Optimization
Wednesday July 27th 2016
Review
2nd derivative test
Textbook reading: Chapter 6.1
Constrained optimization
Review
2nd deri
Review Relations between eigenvalues Practice problems Markov matrices Page rank (or: the 25000000000 $ eigenvector) Pract
Math 415 - Lecture 31
Markov matrices and Google
Thursday July 21st 2016
Review Relations between eigenvalues Practice problems Mark
Review
Least squares
The normal equations
Math 415 - Lecture 24
Least squares
Tuesday July 12th 2016
Applications
Review
Least squares
Textbook reading: Chapter 3.3
The normal equations
Applications
Review
Least squares
The normal equations
Textbook readi
Review
Eigenvectors and eigenvalues
Eigenspaces
How to solve Ax = x
Relations between eigenvalues
Math 415 - Lecture 30
Eigenvectors and Eigenvalues
Wednesday 20th 2016
Practice problems
Review
Eigenvectors and eigenvalues
Eigenspaces
How to solve Ax = x
Review
The QR decomposition
Math 415 - Lecture 26
Orthogonal Matrices and QR Decomposition
Thursday July 14th 2016
Applications of A = QR
Review
The QR decomposition
Textbook reading: Chapter 3.4
Applications of A = QR
Review
The QR decomposition
Textbook
Review
Inner Product and Distances
Inner Product and Angles
Math 415 - Lecture 18
Inner Product and Orthogonality
Tuessday July 5th 2016
Orthogonal vectors
Review
Inner Product and Distances
Inner Product and Angles
Math 415 - Lecture 18
Inner Product and
Review of matrix multiplication
Powers of A
Transpose
Math 415 - Lecture 6
Powers, Transpose, Elementary Matrices
Friday June 17th 2016
Elementary matrices
Review of matrix multiplication
Powers of A
Textbook: Chapter 1.4, 1.5
Transpose
Elementary matrice
Linear independence
Linear independence of matrix columns
Special cases
Math 415 - Lecture 12
Linear independence
Friday June 24th 2016
Additional exercises
Linear independence
Linear independence of matrix columns
Textbook reading: Section 2.3
Special ca
Review
Nonstandard Bases
Matrices for. Polynomials?
Matrices for Linear Transformations
Math 415 - Lecture 17
Linear Transformations
Thursday June 30th 2016
Recap
Review
Nonstandard Bases
Matrices for. Polynomials?
Matrices for Linear Transformations
Math
Review of vector space and subspace
A Shortcut for Determining Subspaces
Math 415 - Lecture 10
Span is a subspace, Null Space
Thursday June 23rd 2016
Null Spaces
Review of vector space and subspace
A Shortcut for Determining Subspaces
Textbook: Chapter 2.
Systems of Linear Equations
Two Fundamental Questions (Existence and Uniqueness)
Math 415 - Lecture 1
Introduction
Monday June 13 2016
Row Reduction and Echelon Forms
Systems of Linear Equations
Two Fundamental Questions (Existence and Uniqueness)
Row Red
Review
The inverse of a matrix
Composition rules
An algorithm for computing the inverse matrix
Math 415 - Lecture 8
February 6th, 2015
Review
The inverse of a matrix
Textbook: Chapter 1.6
Composition rules
An algorithm for computing the inverse matrix
Rev
Review: Solution of linear systems
Math 415 - Lecture 3
January 26th, 2015
Review: Solution of linear systems
Textbook: Chapter 1.2
Review: Solution of linear systems
Textbook: Chapter 1.2
Suggested Practice Exercise: Read section 1.2, do problem 1.3:9
(d
Vector Spaces and Subspaces
Vector Space Examples
MATH 415 Lecture 9
9 February 2015
Subspaces
Vector Spaces and Subspaces
Textbook: Chapter 2.1.
Vector Space Examples
Subspaces
Vector Spaces and Subspaces
Vector Space Examples
Textbook: Chapter 2.1.
Sugg