Positive Semi-Definite Matrix 3: Factorization of Invertible Matrices
Matrix Theory: Let A be an invertible nxn matrix with complex entries. Using the square root result from Part 1, we show that A factors uniquely as PX, where P is unitary and X is (Hermitian) positive definite.
From playlist Matrix Theory
Positive Semi-Definite Matrix 1: Square Root
Matrix Theory: Let A be an nxn matrix with complex entries. Assume that A is (Hermitian) positive semi-definite. We show that A has a unique (Hermitian) positive definite square root; that is, a PSD matrix S such that S^2 = A. The key ingredient is the Spectral Theorem for C^n. Example
From playlist Matrix Theory
Symmetric Matrices and Positive Definiteness
MIT 18.06SC Linear Algebra, Fall 2011 View the complete course: https://ocw.mit.edu/18-06SCF11 Instructor: David Shirokoff A teaching assistant works through a problem on symmetric matrices and positive definiteness. License: Creative Commons BY-NC-SA More information at https://ocw.mit.
From playlist MIT 18.06SC Linear Algebra, Fall 2011
Cubic Curve Sketching (1 of 2: Using Factor Lines to determine regions the curve runs through)
More resources available at www.misterwootube.com
From playlist Further Work with Functions (related content)
Why Does a Negative Times a Negative Equal a Positive
This tutorial uses basic math and logic to demonstrate that a negative times a negative equals a positive. Join this channel to get access to perks: https://www.youtube.com/channel/UCn2SbZWi4yTkmPUj5wnbfoA/join :)
From playlist Basic Math
Proving a Negative Times a Negative Is a Positive with the Distributive Property
When you're multiplying integers and especially when you begin multiplying negative numbers, one of the first questions that comes up for students is why does a negative times a negative equal a positive? There are lots of ways to show it, and a couple of my favorites are: + Multiplicatio
From playlist Math Mini
Vector Calculus 14: The Dot Product Matrix Is Positive Definite
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
What Does It Mean For a Matrix to be POSITIVE? The Practical Guide to Semidefinite Programming(1/4)
Video series on the wonderful field of Semidefinite Programming and its applications. In this first part, we explore the question of how we can generalize the notion of positivity to matrices. -------------------------- Timestamps: 0:00 Intro 0:41 Questions 2:50 Definition 6:09 PSD vs
From playlist Semidefinite Programming
Positive operators. Square roots of operators. Characterization of positive operators. Each positive operator has a unique positive square root.
From playlist Linear Algebra Done Right
Making sense of the confusion matrix
How do you interpret a confusion matrix? How can it help you to evaluate your machine learning model? What rates can you calculate from a confusion matrix, and what do they actually mean? In this video, I'll start by explaining how to interpret a confusion matrix for a binary classifier:
From playlist Machine Learning
How to evaluate a classifier in scikit-learn
In this video, you'll learn how to properly evaluate a classification model using a variety of common tools and metrics, as well as how to adjust the performance of a classifier to best match your business objectives. I'll start by demonstrating the weaknesses of classification accuracy as
From playlist Machine learning in Python with scikit-learn
Bernhard Hanke - Surgery, bordism and scalar curvature
One of the most influential results in scalar curvature geometry, due to Gromov-Lawson and Schoen-Yau, is the construction of metrics with positive scalar curvature by surgery. Combined with powerful tools from geometric topology, this has strong implications for the classification of suc
From playlist Not Only Scalar Curvature Seminar
Special Topics - The Kalman Filter (23 of 55) Finding the Covariance Matrix, Numerical Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate a 3x3 covariance matrix using the deviation matrix method. Next video in this series can be seen at: https://youtu.be/7HWb6N-MRvQ
From playlist SPECIAL TOPICS 1 - THE KALMAN FILTER
Zeros of polynomials via matrix theory and continued fractions - Olga Holtz
Olga Holtz University of California, Berkeley; Member, School of Mathematics February 24, 2014 After a brief review of various classical connections between problems of polynomial zero localization, continued fractions, and matrix theory, I will show a few ways to generalize these classica
From playlist Number Theory
Jintian Zhu - Incompressible hypersurface, positive scalar curvature and positive mass theorem
In this talk, I will introduce a positive mass theorem for asymptotically flat manifolds with fibers (like ALF and ALG manifolds) under an additional but necessary incompressible condition. I will also make a discussion on its connection with surgery theory as well as quasi-local mass and
From playlist Not Only Scalar Curvature Seminar
Structure, function, and evolution of gene regulatory networks by Erik van Nimwegen
Winter School on Quantitative Systems Biology DATE:04 December 2017 to 22 December 2017 VENUE:Ramanujan Lecture Hall, ICTS, Bengaluru The International Centre for Theoretical Sciences (ICTS) and the Abdus Salam International Centre for Theoretical Physics (ICTP), are organizing a Winter S
From playlist Winter School on Quantitative Systems Biology
Moments in positivity:metric positivity,covariance estimation,novel graph invariant by Apoorva Khare
ABSTRACT: I will discuss the connections of matrix positivity and its preservers to multiple sub-fields of mathematics: analysis, metric geometry, combinatorics, and also downstream applications. This includes classical results by Schur, Rudin, Loewner, Karlin, and their students: FitzGera
From playlist ICTS Colloquia
Lecture 12 | Introduction to Robotics
Lecture by Professor Oussama Khatib for Introduction to Robotics (CS223A) in the Stanford Computer Science Department. Professor Khatib shows a short video on An Innovative Space Rover with Extended Climbing Abilities, then continues his lecture on Dynamics. CS223A is an introduction to
From playlist Lecture Collection | Introduction to Robotics
A look at why negative numbers multiply and divide to get positive products or quotients.
From playlist Core Standards - 7th Grade Math
Lecture 6 | Introduction to Robotics
Lecture by Professor Oussama Khatib for Introduction to Robotics (CS223A) in the Stanford Computer Science Department. Professor Khatib shows a short video on Locomotion Gates with Polypod, then lectures on Instantaneous Kinematics and the Jacobian Matrixes. CS223A is an introduction to
From playlist Lecture Collection | Introduction to Robotics