Linear algebra | Determinants | Homogeneous polynomials | Algebra | Matrix theory
In mathematics, the determinant is a scalar value that is a function of the entries of a square matrix. It characterizes some properties of the matrix and the linear map represented by the matrix. In particular, the determinant is nonzero if and only if the matrix is invertible and the linear map represented by the matrix is an isomorphism. The determinant of a product of matrices is the product of their determinants (the preceding property is a corollary of this one).The determinant of a matrix A is denoted det(A), det A, or |A|. In the case of a 2 × 2 matrix the determinant can be defined as Similarly, for a 3 × 3 matrix A, its determinant is Each determinant of a 2 × 2 matrix in this equation is called a minor of the matrix A. This procedure can be extended to give a recursive definition for the determinant of an n × n matrix, known as Laplace expansion. Determinants occur throughout mathematics. For example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants can be used to solve these equations (Cramer's rule), although other methods of solution are computationally much more efficient. Determinants are used for defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. In geometry, the signed n-dimensional volume of a n-dimensional parallelepiped is expressed by a determinant. This is used in calculus with exterior differential forms and the Jacobian determinant, in particular for changes of variables in multiple integrals. (Wikipedia).
(3.2.3) The Determinant of Square Matrices and Properties
This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
From playlist Differential Equations: Complete Set of Course Videos
Ex: Determinant of a 2x2 Matrix
This video provides two examples of calculating a 2x2 determinant. One example contains fractions. Site: http://mathispower4u.com
From playlist The Determinant of a Matrix
This video explains how to find the value of determinants using determinant properties.
From playlist The Determinant of a Matrix
Linear Algebra: Ch 2 - Determinants (1 of 48) What is a Determinant? (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a general definition of “What is a Determinant?” (Part 1) Next video in this series can be seen at: https://youtu.be/vIHnlNjRnGU
From playlist LINEAR ALGEBRA 2: DETERMINANTS
This video explains how to find the value of determinants using determinant properties.
From playlist The Determinant of a Matrix
A more in depth discussion on the determinant of a square matrix.
From playlist Linear Algebra
Characterization of the determinant
In this video, I show why the determinant is so special in math: Namely, it is the only function which is multilinear, alternating, and has the value 1 at the identity matrix. This is a generalization of a previous matrix puzzle for the 2 x 2 case. 2 x 2 case: https://youtu.be/lIMeIC1ZJO8
From playlist Determinants
Equaivalent statements about the determinant. Evaluating elementary matrices.
From playlist Linear Algebra
Linear Algebra 2.3 Properties of Determinants; Cramer’s Rule
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
18. Properties of Determinants
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 18. Properties of Determinants License: Creative Commons BY-NC-SA More information at https://
From playlist MIT 18.06 Linear Algebra, Spring 2005
MATH1050 Lec 25 Determinants College Algebra with Dennis Allison
See full course at: https://cosmolearning.org/courses/college-algebra-pre-calculus-with-dennis-allison/ Video taken from: http://desource.uvu.edu/videos/math1050.php Lecture by Dennis Allison from Utah Valley University.
From playlist UVU: College Algebra with Dennis Allison | CosmoLearning Math
Math 060 Linear Algebra 05 091714: Properties of Determinants
Interaction of determinants and elementary row operations: the "wrong cofactor lemma"; determinants and elementary matrices; invertibility and determinants; determinants of products
From playlist Course 4: Linear Algebra
Oxford Linear Algebra: The Easiest Method to Calculate Determinants
University of Oxford mathematician Dr Tom Crawford explains how to calculate the determinant of a matrix using ERO’s, with a worked example for a 4x4 matrix. Check out ProPrep with a 30-day free trial to see how it can help you to improve your performance in STEM-based subjects: https://w
From playlist Oxford Linear Algebra
Math 060 Linear Algebra 092017 Properties of Determinants
Recall statement of theorem on interaction of elementary row operations and the determinant. Rephrasal of theorem as det(EA) = det(E)det(A) for elementary matrices E. Proof of third part: first "wrong cofactor lemma"; then use lemma to finish proof. Corollary: A is invertible if and onl
From playlist Course 4: Linear Algebra (Fall 2017)
Determinant of an Operator and of a Matrix
Determinant of an operator. An operator is not invertible if and only if its determinant equals 0. Formula for the characteristic polynomial in terms of determinants. Determinant of a matrix. Connection between the two notions of determinant.
From playlist Linear Algebra Done Right
Linear Algebra 14TBD: Overview of the Properties of the Determinant
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 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Linear Algebra: Ch 2 - Determinants (2 of 48) What is a Determinant? (Part 2)
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the notation of and how to calculated a determinant. (Part 2) Next video in this series can be seen at: https://youtu.be/k3ZmxI267Zo
From playlist LINEAR ALGEBRA 2: DETERMINANTS