Multivariable calculus | Linear algebra | Matrix theory

Matrix calculus

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).

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

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

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

Video thumbnail

What is a Matrix?

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

From playlist Intro to Matrices

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

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

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

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

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

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Video thumbnail

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

Related pages

Derivative of the exponential map | Differential equation | Functional analysis | Product rule | Regression analysis | Trace (linear algebra) | Derivative | Gradient | Chain rule | Statistics | Differentiable function | Kronecker delta | Multivariable calculus | Estimation theory | Polynomial | Multivariate normal distribution | Fréchet derivative | Determinant | Conjugate transpose | Partial derivative | Hadamard product (matrices) | Directional derivative | Variable (mathematics) | Row and column vectors | Elliptical distribution | Tangent vector | Mathematics | Function (mathematics) | Vector (mathematics and physics) | Real number | Pushforward (differential) | Euclidean space | Gradient descent | Hessian matrix | Scalar (mathematics) | Symmetric matrix | Taylor series | Tensor | Wiener filter | Calculus | Kronecker product | Ricci calculus | Transpose | Product integral | Kalman filter | Euclidean vector | Matrix (mathematics) | SymPy | Vector calculus | Eigendecomposition of a matrix | Econometrics