Multivariable calculus | Linear algebra | Matrix theory
In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities. This greatly simplifies operations such as finding the maximum or minimum of a multivariate function and solving systems of differential equations. The notation used here is commonly used in statistics and engineering, while the tensor index notation is preferred in physics. Two competing notational conventions split the field of matrix calculus into two separate groups. The two groups can be distinguished by whether they write the derivative of a scalar with respect to a vector as a column vector or a row vector. Both of these conventions are possible even when the common assumption is made that vectors should be treated as column vectors when combined with matrices (rather than row vectors). A single convention can be somewhat standard throughout a single field that commonly uses matrix calculus (e.g. econometrics, statistics, estimation theory and machine learning). However, even within a given field different authors can be found using competing conventions. Authors of both groups often write as though their specific convention were standard. Serious mistakes can result when combining results from different authors without carefully verifying that compatible notations have been used. Definitions of these two conventions and comparisons between them are collected in the section. (Wikipedia).
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
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
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
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
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
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)
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
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!
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
Tensor Calculus Lecture 12a: Linear Transformations in Tensor Notation
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
Polynomials, Matrices and Pascal Arrays | Algebraic Calculus One | Wild Egg
We introduce some basic orientation towards polynomials and matrices in the context of the Pascal-type arrays that figured in our analysis of the Faulhaber polynomials and Bernoulli numbers in the previous video. The key is to observe some beautiful factorizations that occur involving diag
From playlist Algebraic Calculus One from Wild Egg
How to Find the Dimension of a Matrix
How to Find the Dimension of a Matrix If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com My FaceBook Page: https://www.facebook.com/themathsorcerer There are several ways that you can help support my chan
From playlist Matrices
Tensor Calculus 12c: The Self-Adjoint Property in Tensor Notation
This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te
From playlist Introduction to Tensor Calculus
What's New in Calculus & Algebra
I will give an overview of upcoming features related to calculus and algebra in the Wolfram Language. These features include dramatic performance improvements in polynomial algebra functions and in linear algebra for matrices of polynomials, new NFractionalD and NCaputoD functions for nume
From playlist Wolfram Technology Conference 2022
How to Find the Matrix of a Linear Transformation
This is a very elementary discussion of linear transformations and matrices. I mention nothing about bases in this video and just give an easy way to identify the matrix. Hopefully this helps someone. The pencils I used in this video: https://amzn.to/3bCpvpt The paper I used in this video
From playlist Linear Algebra
15. Matrices A(t) Depending on t, Derivative = dA/dt
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k This lecture is ab
From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Proving a Function is One-to-One and Onto
This video gives an example of how to show that a function is both 1-1(injective) and onto(surjective). In other words we show that the function is a one-to-one correspondence(bijection). The example given involves a function which maps the set of all 2 x 2 matrices with real entries into
From playlist Functions, Sets, and Relations
Want to PASS Algebra 2, Pre-Calculus, College Algebra? Better know this….
TabletClass Math: https://tcmathacademy.com/ Pre-Calculus Course: https://tabletclass-academy.teachable.com/p/tabletclass-math-pre-calculus Math help with finding the determinant of a 3 x 3 matrix. For more math help to include math lessons, practice problems and math tutorials check
From playlist Pre-Calculus / Trigonometry
Quadratic Form Minimization: A Calculus-Based Derivation
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 4 Linear Algebra: Inner Products
Using a Matrix Equation to Solve a System of Equations
This video shows how to solve a system of equations by using a matrix equation. The graphing calculator is integrated into the lesson. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Matrix Equations