35 - Properties of bases (continued)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
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
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
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)
Michael Elad: "Sparse Modeling in Image Processing and Deep Learning"
New Deep Learning Techniques 2018 "Sparse Modeling in Image Processing and Deep Learning" Michael Elad, Technion - Israel Institute of Technology, Computer Science Abstract: Sparse approximation is a well-established theory, with a profound impact on the fields of signal and image proces
From playlist New Deep Learning Techniques 2018
The MLE for the weight vector in a Gaussian linear regression model when using basis functions (assuming a known variance). A playlist of these Machine Learning videos is available here: http://www.youtube.com/view_play_list?p=D0F06AA0D2E8FFBA
From playlist Machine Learning
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
Determine the Basis for a Set of Four Vectors in R3
This video explains how to determine the basis of a set of vectors in R3. https://mathispower4u.com
From playlist Linear Independence and Bases
Beating Nyquist with Compressed Sensing
This video shows how it is possible to beat the Nyquist sampling rate with compressed sensing (code in Matlab). Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow Chapter 3 from: "Data-Driven Science and Engineering: Machine Learning,
From playlist Sparsity and Compression [Data-Driven Science and Engineering]
This talk will give an overview of the various optimization functions that can be used to solve a wide variety of convex, nonconvex and multidomain problems. The Wolfram optimization functionality will be demonstrated using a diverse set of examples. Visiting this talk will enable you to s
From playlist Wolfram Technology Conference 2022
Ben Adcock: Compressed sensing and high-dimensional approximation: progress and challenges
Abstract: Many problems in computational science require the approximation of a high-dimensional function from limited amounts of data. For instance, a common task in Uncertainty Quantification (UQ) involves building a surrogate model for a parametrized computational model. Complex physica
From playlist Numerical Analysis and Scientific Computing
Structured Regularization Summer School - A.Hansen - 4/4 - 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
Workshop context setting; Phase transitions in distributed by Partha Mitra
Statistical Physics Methods in Machine Learning DATE: 26 December 2017 to 30 December 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The theme of this Discussion Meeting is the analysis of distributed/networked algorithms in machine learning and theoretical computer science in the "t
From playlist Statistical Physics Methods in Machine Learning
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
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
The Social Context of Philosophy - Ernest Gellner & Bryan Magee (1978)
In this program, Ernest Gellner discusses the social context of modern philosophy with Bryan Magee. This is from a 1978 series on Modern Philosophy called Men of Ideas. #Philosophy #BryanMagee
From playlist Bryan Magee Interviews - Modern Philosophy: Men of Ideas (1977-1978)
Laurent Jacques/Valerio Cambareri: Small width, low distortions: quantized random projections of...
Laurent Jacques / Valerio Cambareri: Small width, low distortions: quantized random projections of low-complexity signal sets Abstract: Compressed sensing theory (CS) shows that a "signal" can be reconstructed from a few linear, and most often random, observations. Interestingly, this rec
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
We've seen before the "standard basis vectors" which both span R^n and are linearly independent. However, these aren't the only sets of vectors that have these two properties. We will define such as a set as being a basis for a given subspace. Learning Objectives: 1) Define a basis. 2) I
From playlist Linear Algebra (Full Course)