Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
Independence, Basis, and Dimension
MIT RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, Fall 2015 View the complete course: http://ocw.mit.edu/RES-18-009F15 Instructor: Gilbert Strang Vectors are a basis for a subspace if their combinations span the whole subspace and are independent:
From playlist MIT Learn Differential Equations
35 - Properties of bases (continued)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Lecture 21. Aligned bases theorem
Notes by Keith Conrad to follow along: https://kconrad.math.uconn.edu/blurbs/linmultialg/modulesoverPID.pdf
From playlist Abstract Algebra 2
We learned about how vectors can form a basis for a vector space, and we can express any vector within a vector space as a linear combination of the basis vectors. But there can be more than one set of basis vectors. What if we want to express a vector using some other basis rather than th
From playlist Mathematics (All Of It)
Linear Algebra - Lecture 30 - Basis of a Subspace
In this video, I give the definition of "basis" for a subspace. Then, I work through the process for finding a basis for the null space and column space of any matrix.
From playlist Linear Algebra Lectures
Linear Algebra - Lecture 31 - Coordinate Systems
In this video, I review the definition of basis, and discuss the notion of coordinates of a vector relative to that basis. The properties of a basis of a subspace guarantee that a vector in that subspace can be written as a linear combination of the basis vectors in only one way. The wei
From playlist Linear Algebra Lectures
11.4.1 The Unit Basis Vectors, One More Time
11.4.1 The Unit Basis Vectors, One More Time
From playlist LAFF Week 11
Stanley Osher: "Compressed Sensing: Recovery, Algorithms, and Analysis"
Graduate Summer School 2012: Deep Learning, Feature Learning "Compressed Sensing: Recovery, Algorithms, and Analysis" Stanley Osher, UCLA Institute for Pure and Applied Mathematics, UCLA July 20, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summe
From playlist GSS2012: Deep Learning, Feature Learning
Lecture 15 | Convex Optimization II (Stanford)
Lecture by Professor Stephen Boyd for Convex Optimization II (EE 364B) in the Stanford Electrical Engineering department. Professor Boyd continues lecturing on L1 Methods for Convex-Cardinality Problems. This course introduces topics such as subgradient, cutting-plane, and ellipsoid met
From playlist Lecture Collection | Convex Optimization
Structured Regularization Summer School - A.Hansen - 3/4 - 20/06/2017
Anders Hansen (Cambridge) Lectures 1 and 2: Compressed Sensing: Structure and Imaging Abstract: The above heading is the title of a new book to be published by Cambridge University Press. In these lectures I will cover some of the main issues discussed in this monograph/textbook. In par
From playlist Structured Regularization Summer School - 19-22/06/2017
Arthur Szlam: "A Tutorial on Sparse Modeling"
Graduate Summer School 2012: Deep Learning Feature Learning A Tutorial on Sparse Modeling" Arthur Szlam, New York University Institute for Pure and Applied Mathematics, UCLA July 16, 2012 For more information: https://www.ipam.ucla.edu/programs/summer-schools/graduate-summer-school-deep
From playlist GSS2012: Deep Learning, Feature Learning
Deep Generative models and Inverse Problems - Alexandros Dimakis
Seminar on Theoretical Machine Learning Topic:Deep Generative models and Inverse Problems Speaker: Alexandros Dimakis Affiliation: University of Texas at Austin Date: April 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
High-dimensional omics data analysis with missing values - Anru Zhang
Virtual Workshop on Missing Data Challenges in Computation Statistics and Applications Topic: High-dimensional omics data analysis with missing values Speaker: Anru Zhang Date: September 10, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Deep Decoder: Concise Image Representations from Untrained Networks (Lecture 2) by Paul Hand
DISCUSSION MEETING THE THEORETICAL BASIS OF MACHINE LEARNING (ML) ORGANIZERS: Chiranjib Bhattacharya, Sunita Sarawagi, Ravi Sundaram and SVN Vishwanathan DATE : 27 December 2018 to 29 December 2018 VENUE : Ramanujan Lecture Hall, ICTS, Bangalore ML (Machine Learning) has enjoyed tr
From playlist The Theoretical Basis of Machine Learning 2018 (ML)
Now we know about vector spaces, so it's time to learn how to form something called a basis for that vector space. This is a set of linearly independent vectors that can be used as building blocks to make any other vector in the space. Let's take a closer look at this, as well as the dimen
From playlist Mathematics (All Of It)
22nd Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series Talk
Date: Wednesday, April 28, 2021, 10:00am Eastern Time Zone (US & Canada) Speaker: Sung Ha Kang, Georgia Tech Title: Vectorization, Decomposition and PDE identification Abstract: This talk covers a few problems in imaging and inverse problems: image vectorization, image decomposition and
From playlist Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS Virtual Seminar Series
Total variation denoising with iterated conditional expectation - Louchet - Workshop 2 - CEB T1 2019
Cécile Louchet (Univ. Orléans) / 12.03.2019 Total variation denoising with iterated conditional expectation. Imaging tasks most often require an energy minimization interpretable in a probabilistic approach as a maximum a posteriori. Taking instead the expectation a posteriori gives an
From playlist 2019 - T1 - The Mathematics of Imaging
CBC data analysis by Anand Sengupta
Discussion Meeting The Future of Gravitational-Wave Astronomy ORGANIZERS: Parameswaran Ajith, K. G. Arun, B. S. Sathyaprakash, Tarun Souradeep and G. Srinivasan DATE: 19 August 2019 to 22 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This discussion meeting, organized in c
From playlist The Future of Gravitational-wave Astronomy 2019
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Basis for a Set of Vectors. In this video, I give the definition for a apos; basis apos; of a set of vectors. I think proceed to work an example that shows thr
From playlist Linear Algebra