Quadratic forms | Linear algebra
In mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x of X for which q(x) = 0. In the theory of real bilinear forms, definite quadratic forms and isotropic quadratic forms are distinct. They are distinguished in that only for the latter does there exist a nonzero null vector. A quadratic space (X, q) which has a null vector is called a pseudo-Euclidean space. A pseudo-Euclidean vector space may be decomposed (non-uniquely) into orthogonal subspaces A and B, X = A + B, where q is positive-definite on A and negative-definite on B. The null cone, or isotropic cone, of X consists of the union of balanced spheres: The null cone is also the union of the isotropic lines through the origin. (Wikipedia).
Null Space: Is a Vector in a Null Space? Find a Basis for a Null Space
This video explains how to determine if a vector is in a null space and how to find a basis for a null space.
From playlist Column and Null Space
Prove a Null Space is a Subspace
This video provides a basic proof that a null space is a subspace.
From playlist Column and Null Space
Null space of a matrix using sympy
In this video I give a brief overview of the null space of a matrix and how to calculate (y hand) the column vectors that will make up the null space of the column. This becomes much easier in sympy, by simply using the nullspace function. If you want to learn more about the null space o
From playlist Modern linear algebra using Python instead of a textbook
From playlist Unlisted LA Videos
The Largest and Smallest Values for the Rank and Nullity of a Matrix (3 x 5)
This video explains how to determine the largest and smallest possible values for the rank and nullity of a 3 by 5 matrix.
From playlist Column and Null Space
Null space of a matrix example
In today's lecture I work through an example to show you a well-known pitfall when it comes to the null space of a matrix. In the example I show you how to create the special cases and how to use them to represent the null space. There is also a quick look at the NullSpace function in Ma
From playlist Introducing linear algebra
In this video I start to discuss the idea of the null space of a matrix. In these situations, the right-hand side of all the equations in the linear system is equal to zero. There is the trivial solution, where all the elements of the solution is zero. We are more interested in the spec
From playlist Introducing linear algebra
Null Space and Column Space of a Matrix
Given a matrix A(ie a linear transformation) there are several important related subspaces. In this video we investigate the Nullspace of A and the column space of A. The null space is the vectors that are "killed" by the transformation - ie sent to zero. The column space will be the image
From playlist Older Linear Algebra Videos
Find a Spanning Vectors (Basis) of the Null Space of a Matrix (Two Vectors)
This video explains how to find a basis or spanning vectors for the null space of a matrix.
From playlist Column and Null Space
Linear Algebra - Lecture 28 - Null Space of a Matrix
In this video lecture, I define the null space of a matrix, and work through several examples.
From playlist Linear Algebra Lectures
Linear Algebra 15o: The Null Space of a Linear Transformation
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 Part 3 Linear Algebra: Linear Transformations
Linear Algebra 15p: The Inverse of a Linear Transformation
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 Part 3 Linear Algebra: Linear Transformations
Review of Ax=b for Differential Equations
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 Partial Differential Equations
9. Independence, Basis, and Dimension
MIT 18.06 Linear Algebra, Spring 2005 Instructor: Gilbert Strang View the complete course: http://ocw.mit.edu/18-06S05 YouTube Playlist: https://www.youtube.com/playlist?list=PLE7DDD91010BC51F8 9. Independence, Basis, and Dimension License: Creative Commons BY-NC-SA More information at h
From playlist MIT 18.06 Linear Algebra, Spring 2005
Visualizations of left nullspace and rowspace | Linear Algebra | Khan Academy
Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/linear-algebra/matrix-transformations/matrix-transpose/v/lin-alg-visualizations-of-left-nullspace-and-rowspace Relationship between left nullspace, rowspace, colum
From playlist Matrix transformations | Linear Algebra | Khan Academy
Linear Algebra 7f2: 21 Easy Null Space Exercises
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 Part 1 Linear Algebra: An In-Depth Introduction with a Focus on Applications
The Largest and Smallest Values for the Rank and Nullity of a Matrix (5 x 3)
This video explains how to determine the largest and smallest possible values for the rank and nullity of a 5 by 3 matrix.
From playlist Column and Null Space
Null space of a matrix | Lecture 21 | Matrix Algebra for Engineers
Definition of the null space of a matrix and how to compute it. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub
From playlist Matrix Algebra for Engineers