Determinants | Functional analysis
In functional analysis, a branch of mathematics, it is sometimes possible to generalize the notion of the determinant of a square matrix of finite order (representing a linear transformation from a finite-dimensional vector space to itself) to the infinite-dimensional case of a linear operator S mapping a function space V to itself. The corresponding quantity det(S) is called the functional determinant of S. There are several formulas for the functional determinant. They are all based on the fact that the determinant of a finite matrix is equal to the product of the eigenvalues of the matrix. A mathematically rigorous definition is via the zeta function of the operator, where tr stands for the functional trace: the determinant is then defined by where the zeta function in the point s = 0 is defined by analytic continuation. Another possible generalization, often used by physicists when using the Feynman path integral formalism in quantum field theory (QFT), uses a functional integration: This path integral is only well defined up to some divergent multiplicative constant. To give it a rigorous meaning it must be divided by another functional determinant, thus effectively cancelling the problematic 'constants'. These are now, ostensibly, two different definitions for the functional determinant, one coming from quantum field theory and one coming from spectral theory. Each involves some kind of regularization: in the definition popular in physics, two determinants can only be compared with one another; in mathematics, the zeta function was used. have shown that the results obtained by comparing two functional determinants in the QFT formalism agree with the results obtained by the zeta functional determinant. (Wikipedia).
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
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
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This video defines the determinant of a matrix and explains what a determinant means in terms of mapping and area. https://mathispower4u.com
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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.
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Equaivalent statements about the determinant. Evaluating elementary matrices.
From playlist Linear Algebra
Oxford Linear Algebra: What is the Determinant Function for a Matrix?
University of Oxford mathematician Dr Tom Crawford explains how to calculate the determinant of a 2x2 and a 3x3 matrix, as well as providing an insight into where the determinant function comes from.** Check out ProPrep with a 30-day free trial to see how it can help you to improve your
From playlist Oxford Linear Algebra
Properties of determinants of matrices | Lecture 31 | Matrix Algebra for Engineers
Fundamental properties of the determinant function. 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_confirmat
From playlist Matrix Algebra for Engineers
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Alexander Bufetov: Determinantal point processes - Lecture 1
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Gap probabilities and Riemann-Hilbert problems in determinantal random point processes - Bertola
Marco Bertola Concordia University November 5, 2013 For more videos, please visit http://video.ias.edu
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Estelle Basor: Toeplitz determinants, Painlevé equations, and special functions. Part I - Lecture 1
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Harini Desiraju: Conformal blocks on a torus via Fredholm determinants
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Evaluating Determinants of a 2x2 and 3x3 Matrix
This video shows how to evaluate 2x2 and 3x3 determinants. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist The Determinant of a Matrix
7: Wronskian Determinant - Dissecting Differential Equations
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