In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
Sketch a Linear Transformation of a Unit Square Given the Transformation Matrix (Shear)
This video explains 2 ways to graph a linear transformation of a unit square on the coordinate plane.
From playlist Matrix (Linear) Transformations
Are Matrix Transformations and Linear Transformation the same? Part I
Learning Objectives: 1) Recognize that we have to categories of transformations, Matrix transformations and Linear Transformations 2) Verify that a given transformation is linear 3) Note that some linear transformations have the same formula as a matrix transformation 4) The big question i
From playlist Linear Algebra (Full Course)
Math 060 102317 Matrix Representations of Linear Transformations III
Review of the construction of the matrix representation of a linear transformation with respect to bases. Review: matrix representation of a linear transformation between Euclidean spaces with respect to bases (not necessarily the standard bases). Example.
From playlist Course 4: Linear Algebra (Fall 2017)
Showing something is a linear transformation Check out my Linear Equations playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmD_u31hoZ1D335sSKMvVQ90 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
From playlist Linear Transformations
Linear Transformations and Linear Systems
In this video we discuss linear transformations. We start by examining the mathematical definition of a linear transformation and apply it to several examples including matrix multiplication and differentiation. We then see how linear transformations relate to linear systems (AKA linear
From playlist Linear Algebra
Suppose you have two bases of the same space and the matrix of a linear transformation with respect to one bases. In this video, I show how to find the matrix of the same transformation with respect to the other basis, without ever having to figure out what the linear transformation does!
From playlist Linear Transformations
This video discusses unitary matrix transformations and how they relate to the geometry of the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: h
From playlist Data-Driven Science and Engineering
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Stanford Seminar - Highly optimized quantum circuits synthesized via data-flow engines
Peter Rakyta, Department of Physics of Complex Systems at Eötvös Loránd University November 9, 2022 The formulation of quantum programs in terms of the fewest number of gate operations is crucial to retrieve meaningful results from the noisy quantum processors accessible these days. In th
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
Pseudo-Unitary Transformations and Solvable Models of Vector Non-Linear....by Pijush K. Ghosh
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Seth Lloyd - Quantum polar decomposition - IPAM at UCLA
Recorded 25 January 2022. Seth Lloyd of the Massachusetts Institute of Technology presents "Quantum polar decomposition" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: The polar decomposition decomposes a matrix into the product of a unitary and an Hermitian matrix. This ta
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Compressed Sensing and Dynamic Mode Decomposition
This video illustrates how to leverage compressed sensing to compute the dynamic mode decomposition (DMD) from under-sampled or compressed data. From the Paper: Compressed Sensing and Dynamic Mode Decomposition. JCD 2(2):165—191, 2015. Steven L. Brunton, Joshua L. Proctor, Jonathan H.
From playlist Research Abstracts from Brunton Lab
Ch 11: What are unitary operators? | Maths of Quantum Mechanics
Hello! This is the eleventh chapter in my series "Maths of Quantum Mechanics." In this episode, we'll define unitary operators and understand how they preserve the inner product. We'll then show how unitary transformations preserve probability in quantum mechanics, and why that makes it a
From playlist Maths of Quantum Mechanics
This lecture discusses the charged free scalar field, and the discrete symmetries P, T, and C, and the CPT theorem.
From playlist UC Davis: Brief Overview of Relativistic Quantum Field Theory
Andras Gilyen - Quantum Algorithms for Quantum Information Processing Tasks - IPAM at UCLA
Recorded 24 January 2022. Andras Gilyen of the Renyi Institute of Mathematics presents "Quantum Algorithms for Quantum Information Processing Tasks" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Quantum linear algebra methods, in particular block-encoding and quantum singu
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022