Канал: mathapptician

Fourier series and Discrete Fourier Transform - part 2

Fourier series and Discrete Fourier Transform - part 2

Fourier series and Discrete Fourier Transform - part 1

Fourier series and Discrete Fourier Transform - part 1

Quick introduction to Fast Fourier Transform

Quick introduction to Fast Fourier Transform

IEEE 754

IEEE 754

Half line example

Half line example

Linear transformation example

Linear transformation example

Associativity of matrix multiplication

Associativity of matrix multiplication

Homogeneous systems

Homogeneous systems

Matrix Properties

Matrix Properties

Elementary row operations

Elementary row operations

Matrix example 1

Matrix example 1

Maximum Cardinality Stable Set Problem

Maximum Cardinality Stable Set Problem

Minimum Weight Spanning Tree LP duality

Minimum Weight Spanning Tree LP duality

Minimum Weight Spanning Tree ILP formulation

Minimum Weight Spanning Tree ILP formulation

Minimum Weight Spanning Tree Problem and algorithms

Minimum Weight Spanning Tree Problem and algorithms

Auxiliary Network

Auxiliary Network

Cunningham's anti cycling rule

Cunningham's anti cycling rule

Obtaining a strongly feasible tree

Obtaining a strongly feasible tree

Minimum Cost Flow Problem

Minimum Cost Flow Problem

Maximum s-t flow part 2 of 2

Maximum s-t flow part 2 of 2

Maximum s t flow part 1 of 2

Maximum s t flow part 1 of 2

Aspects of Edmonds' Blossom Algorithm for perfect matching

Aspects of Edmonds' Blossom Algorithm for perfect matching

Tutte's Matching Theorem and the Tutte-Berge Formula

Tutte's Matching Theorem and the Tutte-Berge Formula

Maximum cardinality matching for bipartite graphs

Maximum cardinality matching for bipartite graphs

Bipartite perfect matching and Hall's Theorem

Bipartite perfect matching and Hall's Theorem

M alternating tree and perfect matching

M alternating tree and perfect matching

Introduction to matchings in undirected graphs

Introduction to matchings in undirected graphs

ILP example with Excel

ILP example with Excel

Linear programming standard form

Linear programming standard form

Chvátal-Gomory cut from tableau example

Chvátal-Gomory cut from tableau example

1 - Linear inequality inference

1 - Linear inequality inference

de Moivre's Theorem tutorial question

de Moivre's Theorem tutorial question

Square roots tutorial question

Square roots tutorial question

Completing the square tutorial question

Completing the square tutorial question

$Decimal to fraction$

Decimal to fraction

Euclidean algorithm for finding GCD

Euclidean algorithm for finding GCD

1 Basic feasible solution

1 Basic feasible solution

1 - Cutting plane example

1 - Cutting plane example

1 - Dual feasible tableau introduction

1 - Dual feasible tableau introduction

1 Sensitivity analysis - cost changes

1 Sensitivity analysis - cost changes

1 - Sensitivity analysis - optimal bases

1 - Sensitivity analysis - optimal bases

Week 6 - Left and right inverses

Week 6 - Left and right inverses

Week 6 - Finding inverse matrices

Week 6 - Finding inverse matrices

Week 6 - Inverse of a product

Week 6 - Inverse of a product

Week 6 - Generating invertible matrices

Week 6 - Generating invertible matrices

Week 2 - Conversion between forms

Week 2 - Conversion between forms

Week 1 - Functions

Week 1 - Functions

Week 11 - Change of basis matrix

Week 11 - Change of basis matrix

Week 5 - Identity matrix

Week 5 - Identity matrix

2 Extreme point optimal solution

2 Extreme point optimal solution

2 Separating hyperplane theorem - special case

2 Separating hyperplane theorem - special case

2 Representations of polytopes

2 Representations of polytopes

3 Decomposition of polyhedra

3 Decomposition of polyhedra

3 Faces of a polyhedron

3 Faces of a polyhedron

4 Total dual integrality

4 Total dual integrality

Week 2 - Complex quadratic equations

Week 2 - Complex quadratic equations

1 Linear Programming Basics

1 Linear Programming Basics

1 Complementary Slackness

1 Complementary Slackness

1 Dual problem in general

1 Dual problem in general

1 Linear Programming Duality

1 Linear Programming Duality

4 Chvátal closure

4 Chvátal closure

4 Integral polyhedra

4 Integral polyhedra

4 Meyer's Theorem for rational polyhedra

4 Meyer's Theorem for rational polyhedra

4 Integer hull

4 Integer hull

4 Linear diophantine equations

4 Linear diophantine equations

3 Minimal faces

3 Minimal faces

2 Polyhedral cones

2 Polyhedral cones

1 Fundamental Theorem of Linear Programming

1 Fundamental Theorem of Linear Programming

1 Fourier Motzkin elimination

1 Fourier Motzkin elimination

1 System of linear inequalities example

1 System of linear inequalities example

1 Certifying infeasibility of a system of linear inequalities

1 Certifying infeasibility of a system of linear inequalities

2 Polytopes

2 Polytopes

2 Pointed polyhedra and lines

2 Pointed polyhedra and lines

2 Extreme points of polyhedra

2 Extreme points of polyhedra

2 Polyhedra

2 Polyhedra

2 Convex hull

2 Convex hull

2 Convex sets

2 Convex sets

2 Optimizing a linear function

2 Optimizing a linear function

3 Facets

3 Facets

2 Carathéodory's Theorem

2 Carathéodory's Theorem

3 Finding the dimension of a polyhedron

3 Finding the dimension of a polyhedron

3 Dimension

3 Dimension

3 Affine subspace and affine hull

3 Affine subspace and affine hull

3 Affine independence

3 Affine independence

3 Subspace of R^n as nullspace

3 Subspace of R^n as nullspace

Kernel of a linear transformation example

Kernel of a linear transformation example

Combining images to a PDF file using LibreOffice

Combining images to a PDF file using LibreOffice

Complex number polar form example

Complex number polar form example

Linear transformation example 1

Linear transformation example 1

Linear transformation example 2

Linear transformation example 2

Checking basis example

Checking basis example

Simple proof example involving eigenvalues

Simple proof example involving eigenvalues

Geometric multiplicity example

Geometric multiplicity example

Cofactor expansion example

Cofactor expansion example

Matrix multiplication example

Matrix multiplication example

Elementary row operations example

Elementary row operations example

Row reduction example 2

Row reduction example 2

Row reduction example 1

Row reduction example 1

Systems of linear equations example 2

Systems of linear equations example 2

Systems of linear equations example 1

Systems of linear equations example 1

Complex numbers example 2

Complex numbers example 2

Complex numbers example 1

Complex numbers example 1

Week 10 - Symmetric matrices and orthogonal diagonalization

Week 10 - Symmetric matrices and orthogonal diagonalization

Week 10 - Orthogonal diagonalization example

Week 10 - Orthogonal diagonalization example

Week 9 - Orthonormal bases

Week 9 - Orthonormal bases

Week 4 - Augmented matrix and row equivalence

Week 4 - Augmented matrix and row equivalence

Pythagorean Theorem - Proof without words

Pythagorean Theorem - Proof without words

Week 1 - What is a field?

Week 1 - What is a field?

Week 1 - Additive and multiplicative inverses

Week 1 - Additive and multiplicative inverses

Week 1 - Set notation

Week 1 - Set notation

Week 2 - Addition and multiplication of complex numbers

Week 2 - Addition and multiplication of complex numbers

Week 6 - Singular matrices

Week 6 - Singular matrices

Week 11 - Linear transformations

Week 11 - Linear transformations

Week 9 - Column space and row space

Week 9 - Column space and row space

Week 9 - Tuple representation

Week 9 - Tuple representation

Week 6 - Transpose of a matrix

Week 6 - Transpose of a matrix

Week 11 - Matrix representations of linear transformations

Week 11 - Matrix representations of linear transformations

Week 11 - Invertible linear transformation

Week 11 - Invertible linear transformation

Week 9 - Dimension of subspaces

Week 9 - Dimension of subspaces

Week 9 - Basis and dimension

Week 9 - Basis and dimension

Week 8 - Linear combination and span

Week 8 - Linear combination and span

Week 8 - Different sets spanning the same set

Week 8 - Different sets spanning the same set

Week 8 - An infinite dimensional vector space

Week 8 - An infinite dimensional vector space

Week 8 - Vector space definition

Week 8 - Vector space definition

Week 8 - Vector space examples and subspaces

Week 8 - Vector space examples and subspaces

Week 8 - Visualizing R^2

Week 8 - Visualizing R^2

Week 8 - Dot product

Week 8 - Dot product

Week 7 - Permutations

Week 7 - Permutations

Week 7 - Properties

Week 7 - Properties

Week 7 - Special matrices

Week 7 - Special matrices

Week 7 - Determinant definition

Week 7 - Determinant definition

Week 7 - Inversions

Week 7 - Inversions

Week 7 - Determinant of a product

Week 7 - Determinant of a product

Week 6 - Matrix Powers

Week 6 - Matrix Powers

Week 6 - Left inverse is right inverse

Week 6 - Left inverse is right inverse

Week 6 - Left and right inverses

Week 6 - Left and right inverses

Week 6 - Matrix Properties

Week 6 - Matrix Properties

Week 5 - Multiple right hand sides

Week 5 - Multiple right hand sides

Week 5 - Associativity of matrix multiplication

Week 5 - Associativity of matrix multiplication

Week 5 - Linear transformation view

Week 5 - Linear transformation view

Week 5 - Row reduction as matrix multiplications

Week 5 - Row reduction as matrix multiplications

Week 5 - Matrix multiplication

Week 5 - Matrix multiplication

Week 4 - Homogeneous system

Week 4 - Homogeneous system

Week 4 - Gauss-Jordan elimination

Week 4 - Gauss-Jordan elimination

Week 4 - Augmented Matrix in RREF

Week 4 - Augmented Matrix in RREF

Week 4 - Reduced row echelon form

Week 4 - Reduced row echelon form

Week 3 - Column view of a system of linear equations

Week 3 - Column view of a system of linear equations

Week 3 - Matrix representations

Week 3 - Matrix representations

Week 3 - Elementary operations

Week 3 - Elementary operations

Week 3 - Method of substitution

Week 3 - Method of substitution

Week 3 - Simple systems

Week 3 - Simple systems

Week 3 - Linear equations introduction

Week 3 - Linear equations introduction

Week 1 - Digital images and matrices

Week 1 - Digital images and matrices

Week 11 - Surjection, injection, bijection

Week 11 - Surjection, injection, bijection

Week 9 - Linear independence

Week 9 - Linear independence

Row chasing in 4 x 4 Lights Out

Row chasing in 4 x 4 Lights Out

Basis and dimension example

Basis and dimension example

Span example 2

Span example 2

Span example 1

Span example 1

Determinant example

Determinant example

GF(2) matrix inverse example

GF(2) matrix inverse example

Complex matrix inverse example

Complex matrix inverse example

Constructive vs Existence Proofs

Constructive vs Existence Proofs

If-and-only-if statement - Proof example

If-and-only-if statement - Proof example

If-and-only-if statements

If-and-only-if statements

Proof Blunder - 2

Proof Blunder - 2

Proof Blunder - 1

Proof Blunder - 1

False Proof Dissected

False Proof Dissected

Mathematical Proofs - A Very Short Introduction

Mathematical Proofs - A Very Short Introduction

Case Analysis Example

Case Analysis Example

Simple Direct Proof Example

Simple Direct Proof Example

Mathematical Induction - Quick Introduction

Mathematical Induction - Quick Introduction

Indirect Proof - Informal Introduction

Indirect Proof - Informal Introduction

Indirect Proof - Example

Indirect Proof - Example

Week 10 - Algebraic and Geometric Multiplicities of an Eigenvalue

Week 10 - Algebraic and Geometric Multiplicities of an Eigenvalue

Week 9 - Basis for nullspace

Week 9 - Basis for nullspace

Week 10 - Diagonalization of an n x n matrix

Week 10 - Diagonalization of an n x n matrix

Week 2- Modulus of a complex number

Week 2- Modulus of a complex number

System of linear inequalities - Example in 2 variables

System of linear inequalities - Example in 2 variables

Week 2 - Finding nth roots of a complex number

Week 2 - Finding nth roots of a complex number

Week 2 - De Moivre's Formula

Week 2 - De Moivre's Formula

Week 2 - Subtraction and division of complex numbers

Week 2 - Subtraction and division of complex numbers

Week 1 - The complex plane

Week 1 - The complex plane

Week 2 - Polar form of a complex number

Week 2 - Polar form of a complex number

Week 7 - Cofactor expansion

Week 7 - Cofactor expansion

Complex equation example

Complex equation example

Week 2 - Euler's identity - an incomplete proof by today's standard

Week 2 - Euler's identity - an incomplete proof by today's standard

Week 2 - Complex conjugate of a complex number

Week 2 - Complex conjugate of a complex number

Week 10 - Recurrence relation and matrix powers

Week 10 - Recurrence relation and matrix powers

Week 9 - Rank-nullity theorem

Week 9 - Rank-nullity theorem

Week 7 - Cramer's rule

Week 7 - Cramer's rule

Week 11 - Kernel of a linear transformation

Week 11 - Kernel of a linear transformation

Week 5 - Elementary matrices example

Week 5 - Elementary matrices example

Week 4 - Solving 3 x 3 Lights Out completely

Week 4 - Solving 3 x 3 Lights Out completely

Week 3 - Setting up a system for Lights Out

Week 3 - Setting up a system for Lights Out

Week 4 - Describing solution sets

Week 4 - Describing solution sets

Week 10 - Eigenvalues and eigenvectors

Week 10 - Eigenvalues and eigenvectors

Week 10 - Matrix Powers Magic

Week 10 - Matrix Powers Magic

Week 1 - Complex numbers

Week 1 - Complex numbers

Week 1 - Modelling Lights Out

Week 1 - Modelling Lights Out