Matrix (mathematics)

In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "2×3-matrix", or a matrix of dimension 2×3. Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. This article focuses on matrices related to linear algebra, and, unless otherwise specified, all matrices represent linear maps or may be viewed as such. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. Square matrices of a given dimension form a noncommutative ring, which is one of the most common examples of a noncommutative ring. The determinant of a square matrix is a number associated to the matrix, which is fundamental for the study of a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and the eigenvalues of a square matrix are the roots of a polynomial determinant. In geometry, matrices are widely used for specifying and representing geometric transformations (for example rotations) and coordinate changes. In numerical analysis, many computational problems are solved by reducing them to a matrix computation, and this often involves computing with matrices of huge dimension. Matrices are used in most areas of mathematics and most scientific fields, either directly, or through their use in geometry and numerical analysis. (Wikipedia).

Matrix (mathematics)
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

What is a Matrix?

What is a matrix? Free ebook

From playlist Intro to Matrices

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: 0:00 Introduction 0:19 Vectors and Matrices 3:30 Identities and Transposes 5:59 Add

From playlist Algebra

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

Matrices lesson 1 - What is a matrix, dimension of a matrix, elements of a matrix.

In this lesson we introduce you to the idea of matrices (an object containing an array of numbers). We also talk about some properties / features of matrices.

From playlist Maths C / Specialist Course, Grade 11/12, High School, Queensland, Australia

Video thumbnail

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

What is a matrix? Join me on Coursera: Lecture notes at Subscribe to my channel:

From playlist Matrix Algebra for Engineers

Video thumbnail

Matrix Addition, Subtraction, and Scalar Multiplication

This video shows how to add, subtract and perform scalar multiplication with matrices.

From playlist Introduction to Matrices and Matrix Operations

Video thumbnail

Matrix Multiplication

This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of matrices. This video deals with multiplying two matrices. For more math videos, visit our channel or go to

From playlist Basics: Matrices

Video thumbnail

Advice for prospective math researchers | Matrices: which exact algorithms should you know?

Algorithms with matrices are at the heart of linear algebra, and are a key resource for prospective research mathematicians, including amateurs. But in fact there is a big distinction in the world of matrix algorithms that is usually finessed, that we want you to be very aware of. That is

From playlist Maxel inverses and orthogonal polynomials (non-Members)

Video thumbnail

Mathematics for ML | Edureka | ML Rewind - 5

🔥Machine Learning Training with Python: This Edureka video on 'Mathematics for Machine Learning' teaches you all the math needed to get started with mastering Machine Learning. It teaches you all the necessary topics and concep

From playlist Machine Learning Tutorial in Python | Edureka

Video thumbnail

VSM, LSA, & SVD | Introduction to Text Analytics with R Part 7

Part 7 of this video series includes specific coverage of: – The trade-offs of expanding the text analytics feature space with n-grams. – How bag-of-words representations map to the vector space model (VSM). – Usage of the dot product between document vectors as a proxy for correlation. –

From playlist Introduction to Text Analytics with R

Video thumbnail

The algebra of nxn matrices | Linear Algebra MATH1141 | N J Wildberger

We introduce the algebra of n by n matrices, concentrating on the 2 by 2 case. The zero and identity matrices are discussed, along with some special types. And we see how this is all a big extension of ordinary arithmetic. ************************ Screenshot PDFs for my videos are availab

From playlist Higher Linear Algebra

Video thumbnail

Advice for research mathematicians | Matrices vs Linear Transformations: which wins? | Wild Egg Math

In the 19th and 20th centuries, the relative importance of matrices and linear transformations changed places. But which is more fundamental? Here is some personal advice for prospective mathematics researchers, especially amateurs, about how to approach certain questions and investigation

From playlist Maxel inverses and orthogonal polynomials (non-Members)

Video thumbnail

Lecture 0809 Principal Component Analysis algorithm

Machine Learning by Andrew Ng [Coursera] 08-02 Dimensionality Reduction

From playlist Machine Learning by Professor Andrew Ng

Video thumbnail

Matrix Expressions and BLAS/LAPACK; SciPy 2013 Presentation

Authors: Rocklin, Matthew, University of Chicago Computer Science Track: General Numeric linear algebra is important ubiquitous. The BLAS/LAPACK libraries include high performance implementations of DLA algorithms in a variety of mathematical situations. They are underused because The i

From playlist Scientific Computing

Video thumbnail

Ideas for a Complex World - Anna Seigal

Science is full of smart tools for explaining the world around us. But those tools can sometimes feel far removed from the way the rest of us understand that world. How can we reconcile the two approaches? Oxford Mathematician Anna Seigal provides some pertinent answers in this Oxford Math

From playlist Oxford Mathematics Public Lectures

Video thumbnail

Benoît Métrot : La PLM et le portail des Mathématiques

Résumé : Utilisation du portail (authentification, création des comptes, les identités). Recording during the thematic meeting : "ANF Mathrice" the October 10, 2016 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this vide

From playlist Services numériques pour les mathématiques

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

Related pages

Wilhelm Jordan (geodesist) | Dimensionality reduction | If and only if | Vector space | Special unitary group | Associative algebra | Indeterminate (variable) | Leibniz formula for determinants | Normal mode | Empty product | Dot product | Density matrix | Linear equation | Covariance matrix | Spin group | Symmetric group | Rational number | Probability vector | Matrix normal distribution | Partial derivative | Game theory | Condition number | William Rowan Hamilton | Polynomial ring | Numerical stability | General linear group | Representation theory | Alfred Tarski | Graph theory | Multiplication | Element (mathematics) | Scalar multiplication | Control theory | Dual space | Square matrix | Equivalence of categories | Real number | Truth table | Euclidean space | Orthonormality | Basis (linear algebra) | Random variable | Special linear group | Hilbert space | Subgroup | Complex number | Hill cipher | Triangular matrix | Matrix multiplication | Independent equation | Reflection (mathematics) | Alfred North Whitehead | Binary operation | Linear differential equation | Computer algebra system | Module (mathematics) | Karl Weierstrass | Matrix field | Unit square | Coding theory | Carl Gustav Jacob Jacobi | Jacobian matrix and determinant | Characteristic polynomial | Finite field | Second derivative | Diagonalizable matrix | Symmetry | Row echelon form | Hermitian matrix | Cyclic permutation | Arthur Cayley | Encryption | Hypercomplex number | Spinor | Gottfried Wilhelm Leibniz | Extension (predicate logic) | Degree of a polynomial | S-matrix | Matrix ring | Zero matrix | Shear mapping | Elementary matrix | Linear map | Scaling (geometry) | Adjugate matrix | Adjacency matrix | Expression (mathematics) | Symbol (formal) | Parallelogram | Monic polynomial | System of linear equations | Addition | Distance matrix | Markov chain | Sparse matrix | Linear least squares | Category (mathematics) | Schur decomposition | Complex conjugate | Limit of a sequence | Dimensionless quantity | Rule of Sarrus | Kronecker product | Axiom | Quadratic form | Numerical analysis | Sylvester equation | Finite element method | Linear system | Logical equivalence | Geometry | Permutation matrix | Partial differential equation | Irregular matrix | Mathematical object | Strassen algorithm | Functional analysis | Pauli matrices | Linear algebra | Ellipse | James Joseph Sylvester | Block matrix | Matrix multiplication algorithm | Spectral theorem | Squeeze mapping | LU decomposition | Generalized inverse | Identity matrix | Linear independence | Matrix norm | Network theory | Geometric transformation | Polynomial | Quark | Determinant | Conjugate transpose | Minor (linear algebra) | Singular value decomposition | Conjugate gradient method | Implicit function theorem | Finite group | Rectangle | Elliptic partial differential equation | Variance | Square root of a matrix | Text mining | Mathematics | Set (mathematics) | Numerical linear algebra | Subtraction | Critical point (mathematics) | Infinity | Hessian matrix | Laplace expansion | Endomorphism ring | Unitary matrix | Bijection | Cabibbo–Kobayashi–Maskawa matrix | Axiom of reducibility | Hyperbola | Logical matrix | Rank–nullity theorem | Regular representation | Jordan normal form | Transpose | Function composition | Image (mathematics) | Commutative ring | Clifford algebra | Rotation matrix | Norm (mathematics) | Algebraically closed field | Absolute value | Gell-Mann matrices | Unit vector | Operation (mathematics) | Coefficient | Quadratic programming | Matrix exponential | Continuous function | Cramer's rule | Differentiable function | Main diagonal | Lorentz group | Group (mathematics) | Number | Quaternion | Diagonal matrix | List of named matrices | Augustin-Louis Cauchy | Gabriel Cramer | Hadamard product (matrices) | Hartree–Fock method | Cayley–Hamilton theorem | Incidence matrix | John von Neumann | Noncommutative ring | Division (mathematics) | Gamma matrices | Sesquilinear form | Commutative property | Fermion | Field (mathematics) | Random matrix | Gotthold Eisenstein | Probability distribution | Ring (mathematics) | Tensor | Descriptive statistics | Number theory | Linear combination | Scalar (mathematics) | Stochastic matrix | Leopold Kronecker | Bilinear form | Symmetric matrix | Infinitesimal | Orthogonal matrix | Transpose of a linear map | Fock matrix | Principia Mathematica | Abstract algebra | Matrix addition | Matrix equivalence | Orthogonal group | Bertrand Russell | Skew-symmetric matrix | Supermatrix | Invertible matrix | Rotation (mathematics)