Numerical analysis | Wavelets

Transfer matrix

In applied mathematics, the transfer matrix is a formulation in terms of a block-Toeplitz matrix of the two-scale equation, which characterizes refinable functions. Refinable functions play an important role in wavelet theory and finite element theory. For the mask , which is a vector with component indexes from to ,the transfer matrix of , we call it here, is defined as More verbosely The effect of can be expressed in terms of the downsampling operator "": (Wikipedia).

Video thumbnail

What is a Matrix?

What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

Video thumbnail

Transfer Functions: Introduction and Implementation

In this video we introduce transfer functions and show how they can be derived from a set of linear, ordinary differential equations. We also examine how to use a transfer function to predict the output of system to a given input. Topics and time stamps: 0:38 – Example using an aircraft

From playlist Control Theory

Video thumbnail

Transfer function matrices

How to represent MIMO systems with transfer function matrices

From playlist Laplace

Video thumbnail

Transpose of matrices

In this very easy and short tutorial I explain the concept of the transpose of matrices, where we exchange rows for columns. The matrices have some properties that you should be aware of. These include how to the the transpose of the product of matrices and in the transpose of the invers

From playlist Introducing linear algebra

Video thumbnail

Column space of a matrix

We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the

From playlist Introducing linear algebra

Video thumbnail

Matrix Addition, Subtraction, and Scalar Multiplication

This video shows how to add, subtract and perform scalar multiplication with matrices. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/

From playlist Introduction to Matrices and Matrix Operations

Video thumbnail

Matrix addition

How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y

From playlist Introducing linear algebra

Video thumbnail

Introduction to Change of Basis Between Two Nonstandard Bases

This video introduces a change of basis and show how to convert between two nonstandard bases.

From playlist Vectors: Change of Basis

Video thumbnail

State Space to Transfer Function

In this video we show how to transform a linear state space representation of a dynamic system to an equivalent transfer function representation. We will derive the transformation of G(s) = C*(s*I-A)^-1*B+D. We will apply this to an example and show how to use Matlab’s various functions

From playlist Control Theory

Video thumbnail

Transfer Function to State Space

In this video we show how to transform a transfer function to an equivalent state space representation. We will derive various transformations such as controllable canonical form, modal canonical form, and controller canonical form. We will apply this to an example and show how to use Ma

From playlist Control Theory

Video thumbnail

Chris Godsil: Problems with continuous quantum walks

Continuous quantum walks are of great interest in quantum computing and, over the last decade, my group has been studying this topic intensively. As graph theorists, one of our main goals has been to get a better understanding of the relation between the properties of a walk and the proper

From playlist Combinatorics

Video thumbnail

Basic Lectures on Bethe Ansatz (Pedagogical Lecture 03) by Fabio Franchini

PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore

From playlist Integrable​ ​systems​ ​in​ ​Mathematics,​ ​Condensed​ ​Matter​ ​and​ ​Statistical​ ​Physics

Video thumbnail

Non-Hermitian Hamiltonians and Low-Energy Scattering in one Dimension by Ali Mostafazadeh

PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a

From playlist Non-Hermitian Physics (ONLINE)

Video thumbnail

Matrix Addition and Scalar Multiplication

This is the first video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with matrix dimensions, matrix addition, and scalar multiplication. For more math videos, visit our channel or go to www.centerofmath.org

From playlist Basics: Matrices

Video thumbnail

Lecture 4 (CEM) -- Transfer Matrix Method

This method introduces the simple 1D transfer matrix method. It starts with Maxwell's equations and steps the student up to the equation for the transfer matrix and how to calculate the global transfer matrix. Reasons are then explained for why the method is inherently unstable. Prerequ

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Video thumbnail

Lecture 19 (CEM) -- Formulation of Rigorous Coupled-Wave Analysis

This lecture steps the student through the formulation of rigorous coupled-wave analysis. It parallels the lecture on the transfer matrix method and adopts the same formalism for scattering matrices. A bonus section discusses the enhanced transmittance matrix approach. Prerequisite Lect

From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering

Video thumbnail

Thin Lens Ray Transfer Matrix

https://www.patreon.com/edmundsj If you want to see more of these videos, or would like to say thanks for this one, the best way you can do that is by becoming a patron - see the link above :). And a huge thank you to all my existing patrons - you make these videos possible. Here I derive

From playlist Geometric Optics

Video thumbnail

Time-independent scattering theory (Pedagogical talk) – Lecture - 01 by Ali Mostafazadeh

DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Physics. The scope of the program on Non-H

From playlist Non-Hermitian Physics - PHHQP XVIII

Video thumbnail

Version 1: Find the Dimensions of the Transformation Matrix Given T(x)=b

This video explains how to determine the dimensions of a linear transformation matrix when given T(x)=b.

From playlist Matrix (Linear) Transformations

Related pages

Spectral radius | Euclidean algorithm | Sylvester matrix | Determinant | Fast Fourier transform | Refinable function | Resultant | Trace (linear algebra) | Wavelet | Hurwitz determinant | Upsampling | Modular arithmetic | Convolution | Applied mathematics