The Hessian matrix | Multivariable calculus | Khan Academy
The Hessian matrix is a way of organizing all the second partial derivative information of a multivariable function.
From playlist Multivariable calculus
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Visualization of tensors - part 1
This video visualizes tensors. It shows some introduction to tensor theory and demonstrates it with the Cauchy stress tensor. Future parts of this series will show more theory and more examples. It talks about the term 'tensor' as used in physics and math. In the field of AI the term 'te
From playlist Animated Physics Simulations
Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
Symmetric matrices - eigenvalues & eigenvectors
Free ebook http://tinyurl.com/EngMathYT A basic introduction to symmetric matrices and their properties, including eigenvalues and eigenvectors. Several examples are presented to illustrate the ideas. Symmetric matrices enjoy interesting applications to quadratic forms.
From playlist Engineering Mathematics
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Jorge Nocedal: "Tutorial on Optimization Methods for Machine Learning, Pt. 2"
Graduate Summer School 2012: Deep Learning, Feature Learning "Tutorial on Optimization Methods for Machine Learning, Pt. 2" Jorge Nocedal, Northwestern University Institute for Pure and Applied Mathematics, UCLA July 19, 2012 For more information: https://www.ipam.ucla.edu/programs/summ
From playlist GSS2012: Deep Learning, Feature Learning
Jorge Nocedal: "Tutorial on Optimization Methods for Machine Learning, Pt. 1"
Graduate Summer School 2012: Deep Learning, Feature Learning "Tutorial on Optimization Methods for Machine Learning, Pt. 1" Jorge Nocedal, Northwestern University Institute for Pure and Applied Mathematics, UCLA July 19, 2012 For more information: https://www.ipam.ucla.edu/programs/summ
From playlist GSS2012: Deep Learning, Feature Learning
Lecture 12-Jack Simons Electronic Structure Theory- Gradients and reaction paths
Response theory; molecular deformation gradients and Hessians; reaction paths. (1)Jack Simons Electronic Structure Theory- Session 1- Born-Oppenheimer approximation http://www.youtube.com/watch?v=Z5cq7JpsG8I (2)Jack Simons Electronic Structure Theory- Session 2- Hartree-Fock http://w
From playlist U of Utah: Jack Simons' Electronic Structure Theory course
Harvard AM205 video 4.9 - Quasi-Newton methods
Harvard Applied Math 205 is a graduate-level course on scientific computing and numerical methods. The previous video in this series discussed using the Newton method to find local minima of a function; while this method can be highly efficient, it requires the exact Hessian of the functio
From playlist Optimizers in Machine Learning
In this video we discuss unconstrained optimization. We will review how to find maxima and minima for 1 dimensional function by finding where the slope is equal to zero and then checking the sign of the second derivative to determine if this is a maxima or minima. We then extend this ide
From playlist Optimization
Aaron Sidford: Introduction to interior point methods for discrete optimization, lecture II
Over the past decade interior point methods (IPMs) have played a pivotal role in mul- tiple algorithmic advances. IPMs have been leveraged to obtain improved running times for solving a growing list of both continuous and combinatorial optimization problems including maximum flow, bipartit
From playlist Summer School on modern directions in discrete optimization
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
(ML 9.6) MLE for linear regression (part 3)
Computing the MLE for the weight vector in a Gaussian linear regression model, 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
This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
M4ML - Multivariate Calculus - 2.7 The Hessian
Welcome to the “Mathematics for Machine Learning: Multivariate Calculus” course, offered by Imperial College London. This video is part of an online specialisation in Mathematics for Machine Learning (m4ml) hosted by Coursera. For more information on the course and to access the full ex
From playlist Mathematics for Machine Learning - Multivariate Calculus