# Multilinear algebra

Multilinear algebra is a subfield of mathematics that extends the methods of linear algebra. Just as linear algebra is built on the concept of a vector and develops the theory of vector spaces, multilinear algebra builds on the concepts of p-vectors and multivectors with Grassmann algebras. (Wikipedia).

Multilinear Algebra

Multilinearity of the determinant In this video, I define the notion of a multilinear function and I show that the determinant is multilinear. Come and get a taste of the beauty of multilinear algebra :) Check out my Determinants Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIr

From playlist Determinants

Multivariable Calculus: Cross Product

In this video we explore how to compute the cross product of two vectors using determinants.

From playlist Multivariable Calculus

Local linearity for a multivariable function

A visual representation of local linearity for a function with a 2d input and a 2d output, in preparation for learning about the Jacobian matrix.

From playlist Multivariable calculus

Multivariable Calculus | Transformations of the plane.

Working towards a formula for change of variables in multiple integrals, we introduce the notion of a one to one transformation of the plane. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus | Multiple Integrals

15_4_1 Example problem with the line integral of a multivariable functions

In this example problem I look at solving a line integral of a multivariable function with respect to a coordinate variable.

From playlist Advanced Calculus / Multivariable Calculus

Duality in Linear Algebra: Dual Spaces, Dual Maps, and All That

An exploration of duality in linear algebra, including dual spaces, dual maps, and dual bases, with connections to linear and bilinear forms, adjoints in real and complex inner product spaces, covariance and contravariance, and matrix rank. More videos on linear algebra: https://youtube.c

From playlist Summer of Math Exposition Youtube Videos

Quantitative Inverse Theorem for Gowers Uniformity Norms š¯–´5 and š¯–´6 in š¯”½n2 - Luka Milicevic

Workshop on Additive Combinatorics and Algebraic Connections Topic: Quantitative Inverse Theorem for Gowers Uniformity Norms š¯–´5 and š¯–´6 in š¯”½n2 Speaker: Luka Milicevic Affiliation: Serbian Academy of Sciences and Arts Date: October 27, 2022Ā  In this talk, I will discuss a proof of a quant

From playlist Mathematics

QED Prerequisites Geometric Algebra 13 Tensors

In this lesson we make contact with the standard concept of tensors using spacetime algebra. Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://apps.apple.com/us/app/vittle-pro-video-whit

From playlist QED- Prerequisite Topics

Jason P. Bell: Applications of algebra to automatic sequences and pattern avoidance - Lecture 1

Abstract: We will cover some of the more important results from commutative and noncommutative algebra as far as applications to automatic sequences, pattern avoidance, and related areas. Well give an overview of some applications of these areas to the study of automatic and regular sequen

From playlist Mathematical Aspects of Computer Science

15_4_3 Example problem with the line integrals of a multivariable functions

In this example problem I look at solving a line integral of a multivariable function with respect to a coordinate variable.

From playlist Advanced Calculus / Multivariable Calculus

Multivariable Calculus | What is a vector field.

We introduce the notion of a vector field and give some graphical examples. We also define a conservative vector field with examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

Worldwide Calculus: Euclidean Space

Lecture on 'Euclidean Space' from 'Worldwide Multivariable Calculus'. For more lecture videos and \$10 digital textbooks, visit www.centerofmath.org.

From playlist Multivariable Spaces and Functions

Jonathan Belcher: Bridge cohomology-a generalization of Hochschild and cyclic cohomologies

Talk by Jonathan Belcher in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-... on August 12, 2020.

From playlist Global Noncommutative Geometry Seminar (Americas)

Open Quantum Kirwan Map - Guangbo Xu

Princeton/IAS Symplectic Geometry Seminar Topic: Open Quantum Kirwan Map Speaker: Guangbo Xu Affiliation: Visiting Professor, School of Mathematics Date: March 26, 2018 For more videos, please visitĀ http://video.ias.edu

From playlist Mathematics

Antonio Lerario: Random algebraic geometry - Lecture 4

CONFERENCE Recording during the thematic meeting : "Real Algebraic Geometry" the October 27, 2022 at the Centre International de Rencontres MathĆ©matiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio

From playlist Algebraic and Complex Geometry

Lek-Heng Lim: "What is a tensor? (Part 2/2)"

Watch part 1/2 here: https://youtu.be/MkYEh0UJKcE Tensor Methods and Emerging Applications to the Physical and Data Sciences Tutorials 2021 "What is a tensor? (Part 2/2)" Lek-Heng Lim - University of Chicago, Statistics Abstract: We discuss the three best-known definitions of a tensor:

HĆ¼lya ArgĆ¼z - Gromov-Witten Theory of Complete Intersections 1/3

I will describe an inductive algorithm computing Gromov-Witten invariants in all genera with arbitrary insertions of all smooth complete intersections in projective space. This uses a monodromy analysis, as well as new degeneration and splitting formulas for nodal Gromov--Witten invariants

From playlist Workshop on Quantum Geometry

15_4_2 Example problem with the line integral of a multivariable functions

In this example problem I look at solving a line integral of a multivariable function with respect to a coordinate variable.

From playlist Advanced Calculus / Multivariable Calculus

The Complexity of Multilinear Averages - Frederick Manners

Workshop on Dynamics, Discrete Analysis and Multiplicative Number Theory Topic: The Complexity of Multilinear Averages Speaker: Frederick Manners Affiliation: Von Neumann Fellow, School of Mathematics Date: February 28, 2023 A central question in additive combinatorics is to determine wh

From playlist Mathematics