Matrix theory | Signal processing
In linear algebra, the coherence or mutual coherence of a matrix A is defined as the maximum absolute value of the cross-correlations between the columns of A. Formally, let be the columns of the matrix A, which are assumed to be normalized such that The mutual coherence of A is then defined as A lower bound is A deterministic matrix with the mutual coherence almost meeting the lower bound can be constructed by . This concept was reintroduced by David Donoho and Michael Elad in the context of sparse representations. A special case of this definition for the two-ortho case appeared earlier in the paper by Donoho and Huo. The mutual coherence has since been used extensively in the field of sparse representations of signals. In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identify the true representation of a sparse signal. Joel Tropp introduced a useful extension of Mutual Coherence, known as the Babel function, which extends the idea of cross-correlation between pairs of columns to the cross-correlation from one column to a set of other columns. The Babel function for two columns is exactly the Mutual coherence, but it also extends the coherence relationship concept in a way that is useful and relevant for any number of columns in the sparse representation matix as well. (Wikipedia).
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
Consistency of a System of Linear Equations
Linear Algebra: Determine whether the following systems of linear equations are consistent: (a) x -3y +2z + 2w = 1, 2x - 2z = 3, 4x - 6y +2z + 4w = 6; (b) x-3y+2z+2w=1, 2x-2z = 3, 4x - 6y - 2z + 4w = 5.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
This educational video delves into how you quantify a linear statistical relationship between two variables using covariance! #statistics #probability #SoME2 This video gives a visual and intuitive introduction to the covariance, one of the ways we measure a linear statistical relation
From playlist Summer of Math Exposition 2 videos
What is a Coordinate Covalent Bond?
This chemistry video tutorial provides a basic introduction into coordinate covalent bond. Line any covalent bond, electrons are shared. However, in a coordinate covalent bond, one atom donates both electrons that contribute to the formation of the bond. A lewis acid lewis base reaction
From playlist New AP & General Chemistry Video Playlist
Math 060 092717 Linear Independence
Linear independence: definition of, examples and non-examples; intuition (dependence is redundancy; independence is minimality). Equivalence of dependence and a vector being included in the span of the others. Equivalence of independence with every vector in the span being uniquely expre
From playlist Course 4: Linear Algebra (Fall 2017)
In this first video on cosets, I show you the equivalence relation on a group, G, that will turn out to create equivalence classes, which are actually cosets. We will prove later that these equivalence classes created by an element in the group, G, are equal to the set of element made up
From playlist Abstract algebra
Geordie Williamson: Langlands and Bezrukavnikov II Lecture 17
SMRI Seminar Series: 'Langlands correspondence and Bezrukavnikov’s equivalence' Geordie Williamson (University of Sydney) Abstract: The second part of the course focuses on affine Hecke algebras and their categorifications. Last year I discussed the local Langlands correspondence in bro
From playlist Geordie Williamson: Langlands correspondence and Bezrukavnikov’s equivalence
Equivariantization and de-equivariantization - Shotaro Makisumi
Geometric and Modular Representation Theory Seminar Topic: Equivariantization and de-equivariantization Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: February 10, 2021 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory
Quantum Mechanics -- a Primer for Mathematicians
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From playlist Mathematics
Linear algebra is the branch of mathematics concerning linear equations such as linear functions and their representations through matrices and vector spaces. Linear algebra is central to almost all areas of mathematics. Topic covered: Vectors: Basic vectors notation, adding, scaling (0:0
From playlist Linear Algebra
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Visit http://ilectureonline.com for more math and science lectures! To donate:a http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn the difference between the variance and the covariance. A variance (s^2) is a measure of how spread out the numbers of
From playlist COVARIANCE AND VARIANCE
In this video we continue discussing congruences and, in particular, we discuss solutions of linear congruences. The content of this video corresponds to Section 4.4 of my book "Number Theory and Geometry" which you can find here: https://alozano.clas.uconn.edu/number-theory-and-geometry/
From playlist Number Theory and Geometry
Quantum Noise and Information Scrambling in Multi-Qubit Evolution by V Subrahmanyam
DISCUSSION MEETING STATISTICAL PHYSICS: RECENT ADVANCES AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Sakuntala Chatterjee (SNBNCBS, Kolkata), Kavita Jain (JNCASR, Bangalore) and Tridib Sadhu (TIFR, Mumbai) DATE: 14 February 2022 to 15 February 2022 VENUE: Online In the past few decades,
From playlist Statistical Physics: Recent advances and Future directions (ONLINE) 2022
Dimensionality Reduction | Stanford CS224U Natural Language Understanding | Spring 2021
For more information about Stanford's Artificial Intelligence professional and graduate programs visit: https://stanford.io/ai To learn more about this course visit: https://online.stanford.edu/courses/cs224u-natural-language-understanding To follow along with the course schedule and sy
From playlist Stanford CS224U: Natural Language Understanding | Spring 2021
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From playlist Mathematics
Jacob Lurie: A Riemann-Hilbert Correspondence in p-adic Geometry Part 2
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From playlist Felix Klein Lectures 2022
Matteo Gori - 2nd-Quantization of Many-Body Dispersion Formalism: Modeling of Million Atom Systems
Recorded 01 April 2022. Matteo Gori of the University of Luxembourg Department of Science and Materials presents "Second-Quantization of Many-Body Dispersion Formalism: Towards Modeling of Million Atom Systems in Arbitrary Environments" at IPAM's Multiscale Approaches in Quantum Mechanics
From playlist 2022 Multiscale Approaches in Quantum Mechanics Workshop
Verlinde Dimension Formula for the Space of Conformal Blocks and the moduli of G...V- Shrawan Kumar
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From playlist Mathematics
[Linear Algebra] Eigenspaces and Linear Independence
Introduce the concept of Eigenspaces, and then show that if a set of vectors corresponds to distinct eigenvalues, then the set of vectors is linearly independent. LIKE AND SHARE THE VIDEO IF IT HELPED! Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW L
From playlist Linear Algebra