Linear algebra

Matrix pencil

In linear algebra, if are complex matrices for some nonnegative integer , and (the zero matrix), then the matrix pencil of degree is the matrix-valued function defined on the complex numbers A particular case is a linear matrix pencil with where and are complex (or real) matrices. We denote it briefly with the notation . A pencil is called regular if there is at least one value of such that . We call eigenvalues of a matrix pencil all complex numbers for which (see eigenvalue for comparison). The set of the eigenvalues is called the spectrum of the pencil and is written .Moreover, the pencil is said to have one or more eigenvalues at infinity if has one or more 0 eigenvalues. (Wikipedia).

Video thumbnail

Definition of a matrix | Lecture 1 | Matrix Algebra for Engineers

What is a matrix? Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1

From playlist Matrix Algebra for Engineers

Video thumbnail

Understanding Matrices and Matrix Notation

In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start

From playlist Mathematics (All Of It)

Video thumbnail

What is a Matrix?

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

From playlist Intro to Matrices

Video thumbnail

Linear Algebra for Computer Scientists. 12. Introducing the Matrix

This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order

From playlist Linear Algebra for Computer Scientists

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 Matrices | Geometry | Maths | FuseSchool

Introduction to Matrices | Geometry | Maths | FuseSchool Chances are, you have heard the word “matrices” in a movie. But do you know what they are or what they are used for? Well, “matrices” is plural of a “matrix”. And you can think about a matrix as just a table of numbers, and that’s

From playlist MATHS: Geometry & Measures

Video thumbnail

2 Construction of a Matrix-YouTube sharing.mov

This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.

From playlist Linear Algebra

Video thumbnail

Nijenhuis geometry for ECRs: Pre-recorded Lecture 4

Pre-recorded Lecture 4: Nijenhuis geometry for ECRs Date: 10 February 2022 Lecture slides: https://mathematical-research-institute.sydney.edu.au/wp-content/uploads/2022/02/Prerecorded_Lecture4.pdf ---------------------------------------------------------------------------------------------

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems

Video thumbnail

Pre-recorded lecture 18: Nijenhuis pencils and second cohomology theory

MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

Video thumbnail

WildLinAlg10: Equations of lines and planes in 3D

This video shows how we work with lines in the plane and planes in 3D space in Linear Algebra. A line in 2D is represented by a linear equation in x and y, a plane in 3D by a linear equation in x,y and z. Both can also be described in parametric form. It is important to be able to change f

From playlist A first course in Linear Algebra - N J Wildberger

Video thumbnail

Seminar on Applied Geometry and Algebra (SIAM SAGA): Bernd Sturmfels

Date: Tuesday, February 9 at 11:00am EST (5:00pm CET) Speaker: Bernd Sturmfels, MPI MiS Leipzig / UC Berkeley Title: Linear Spaces of Symmetric Matrices. Abstract: Real symmetric matrices appear ubiquitously across the mathematical sciences, and so do linear spaces of such matrices. We

From playlist Seminar on Applied Geometry and Algebra (SIAM SAGA)

Video thumbnail

How to Quickly Create a Matrix in GeoGebra; How to Multiply 2 Matrices

Creating a matrix in GeoGebra is EASY. You need to use the LIST icons { }. In GeoGebra, a matrix is actually a sequence of lists within a single list. This video shows how.

From playlist Algebra 1: Dynamic Interactives!

Video thumbnail

Pre-recorded lecture 22: Open problems (part 2)

MATRIX-SMRI Symposium: Nijenhuis Geometry and integrable systems Pre-recorded lecture: These lectures were recorded as part of a cooperation between the Chinese-Russian Mathematical Center (Beijing) and the Moscow Center of Fundamental and Applied Mathematics (Moscow). Nijenhuis Geomet

From playlist MATRIX-SMRI Symposium: Nijenhuis Geometry companion lectures (Sino-Russian Mathematical Centre)

Video thumbnail

Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems Lecture 5

Ren-Cang Li from UT presents: Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems; Lecture 5

From playlist Gene Golub SIAM Summer School Videos

Video thumbnail

Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems, Lecture 3

Ren-Cang Li from UT presents: Rayleigh Quotient Based Numerical Methods for Eigenvalue Problems; Lecture 3

From playlist Gene Golub SIAM Summer School Videos

Video thumbnail

Linear Algebra 4 : Multiplying Matrices

New Video Everyday!!! [ Click Notification Bell ] Quizzes for Linear Algebra Videos : http://bit.ly/LAQuizzes This video is all about multiplying matrices. We multiply scalars and matrices times matrices. I show a real world example on how this is useful. I then cover identity and invers

From playlist 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

Squares represented by a product of three ternary (...) - Harpaz - Workshop 2 - CEB T2 2019

Yonatan Harpaz (Université Paris Nord) / 27.06.2019 Squares represented by a product of three ternary quadratic forms, and a homogeneous variant of a method of Swinnerton-Dyer. Let k be a number field. In this talk we will consider K3 surfaces over k which admit a degree 2 map to the pr

From playlist 2019 - T2 - Reinventing rational points

Video thumbnail

Orthogonal Matrix Exercises — Topic 25 of Machine Learning Foundations

In this quick video from my Machine Learning Foundations series, I present a series of paper-and-pencil exercises that test your comprehension of the orthogonal matrix properties covered in the preceding video, as well as many of the other key matrix properties we covered earlier on. The

From playlist Linear Algebra for Machine Learning

Video thumbnail

Matrix Algebra Basics || Matrix Algebra for Beginners

In mathematics, a matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns. This course is about basics of matrix algebra. Website: https://geekslesson.com/ 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add

From playlist Algebra

Related pages

Quadratic eigenvalue problem | Generalized pencil-of-function method | Rayleigh quotient | Linear algebra | QR algorithm | Nonlinear eigenproblem | Matrix (mathematics) | Numerical linear algebra