Singular value decomposition | Linear algebra | Matrix theory

Orthogonal Procrustes problem

The orthogonal Procrustes problem is a matrix approximation problem in linear algebra. In its classical form, one is given two matrices and and asked to find an orthogonal matrix which most closely maps to . Specifically, where denotes the Frobenius norm. This is a special case of Wahba's problem (with identical weights; instead of considering two matrices, in Wahba's problem the columns of the matrices are considered as individual vectors). Another difference is, that Wahba's problem tries to find a proper rotation matrix, instead of just an orthogonal one. The name Procrustes refers to a bandit from Greek mythology who made his victims fit his bed by either stretching their limbs or cutting them off. (Wikipedia).

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34. Distance Matrices, Procrustes Problem

MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018 Instructor: Gilbert Strang View the complete course: https://ocw.mit.edu/18-065S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63oMNUHXqIUcrkS2PivhN3k This lecture conti

From playlist MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018

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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

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Joshua Mike (6/15/20): TALLEM: Topological Assembly of Locally Linear Euclidean Models

Title: TALLEM: Topological Assembly of Locally Linear Euclidean Models Abstract: We present a new topological data analysis tool for nonlinear dimensionality reduction. This method, dubbed TALLEM, assembles a collection of local Euclidean coordinates, and leverages ideas from the theory o

From playlist ATMCS/AATRN 2020

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Physics-Informed Dynamic Mode Decomposition (PI-DMD)

In this video, Peter Baddoo from MIT (www.baddoo.co.uk) explains how physical laws can be integrated into the dynamic mode decomposition. Title: Physics-informed dynamic mode decomposition (piDMD) Authors: Peter J. Baddoo, Benjamin Herrmann, Beverley J. McKeon, J. Nathan Kutz, and Steven

From playlist Research Abstracts from Brunton Lab

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AGACSE2021 Joan Lasenby - GA approach to orthogonal transformations in signal and image processing.

Professor Joan Lasenby from Cambridge University on a Geometric Algebra approach to orthogonal transformations and their use in signal and image processing.

From playlist AGACSE2021

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Edoardo Ponti & Yova Kementchedjhieva (#botsBerlin Meetup)

Welcome to the livestream of BotsBerlin! This is our Deep Tech meet-up, where we encourage the discussion of tech and research in the bot-building world. We are very grateful to be having Edoardo Ponti from the University of Cambridge and Yova Kementchedjhieva from the University of Cope

From playlist Deep Tech Meetup

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Determining adjacent angles

👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships

From playlist Angle Relationships From a Figure

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Biologically relevant distances between morphological surfaces representing teeth and bones

Distinguished Visitor Lecture Series Biologically relevant distances between morphological surfaces representing teeth and bones Ingrid Daubechies Duke University, USA

From playlist Distinguished Visitors Lecture Series

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Ingrid Daubechies: "Bones, Teeth and Animation"

Green Family Lecture Series "Bones, Teeth and Animation" Ingrid Daubechies, Duke University Abstract: The talk describes new distances between pairs of two-dimensional surfaces (embedded in three-dimensional space) that use both local structures and global information in the surfaces. Th

From playlist Public Lectures

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JASP 0.14 Tutorial: Dealing with Missing Values (Episode 32)

In this JASP tutorial, I discuss how JASP deals with missing values, including various notation methods and casewise vs. listwise deletion in the even to multiple missing values in your dataset. The data in this video can be found in the base JASP Data Library. JASP: https://jasp-stats.o

From playlist JASP Tutorials

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How to Determine Alternate Interior Angles

👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

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Learn How to Identify Alternative Exterior Angles

👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

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Orthogonal Projections

In this video, I define the concept of orthogonal projection of a vector on a line (and on more general subspaces), derive a very nice formula for it, and show why orthogonal projections are so useful. You might even see the hugging formula again. Enjoy! This is the second part of the ort

From playlist Orthogonality

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Determine the values of two angles that lie on a lie with a third angle

👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships

From playlist Angle Relationships From a Figure

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Learn to Find Corresponding Angles From a Figure

👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

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Properties of Parallelograms

I introduce the Properties of Parallelograms...the opposite sides are equal, the opposite angles are equal, the consecutive angles are supplementary, and the diagonals bisect each other. I work through four algebraic examples in this video at 4:28 14:30 Find free review test, useful notes

From playlist Geometry

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Determining Two Angles are Consecutive Interior Angles from a Figure

👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

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How to determine two acute adjacent angles from a figure

👉 Learn how to define and classify different angles based on their characteristics and relationships are given a diagram. The different types of angles that we will discuss will be acute, obtuse, right, adjacent, vertical, supplementary, complementary, and linear pair. The relationships

From playlist Angle Relationships From a Figure

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Katharine Turner: Statistical Shape Analysis using the Persistent Homology Transform

The lecture was held within the framework of the Hausdorff Trimester Program : Applied and Computational Algebraic Topology

From playlist HIM Lectures: Special Program "Applied and Computational Algebraic Topology"

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The Angles Created from Lines and a Transversal

👉 Learn how to identify angles from a figure. This video explains how to solve problems using angle relationships between parallel lines and transversal. We'll determine the solution given, corresponding, alternate interior and exterior. All the angle formed by a transversal with two paral

From playlist Parallel Lines and a Transversal

Related pages

Procrustes analysis | Rotation matrix | Orthogonal matrix | Frobenius inner product | Wahba's problem | Linear algebra | Determinant | Singular value decomposition | Procrustes transformation | Matrix (mathematics) | Kabsch algorithm