Multilinear algebra | Tensors | Geometric algebra | Differential geometry
In multilinear algebra, a multivector, sometimes called Clifford number, is an element of the exterior algebra ฮ(V) of a vector space V. This algebra is graded, associative and alternating, and consists of linear combinations of simple k-vectors (also known as decomposable k-vectors or k-blades) of the form where are in V. A k-vector is such a linear combination that is homogeneous of degree k (all terms are k-blades for the same k). Depending on the authors, a "multivector" may be either a k-vector or any element of the exterior algebra (any linear combination of k-blades with potentially differing values of k). In differential geometry, a k-vector is a vector in the exterior algebra of the tangent vector space; that is, it is an antisymmetric tensor obtained by taking linear combinations of the exterior product of k tangent vectors, for some integer k โฅ 0. A differential k-form is a k-vector in the exterior algebra of the dual of the tangent space, which is also the dual of the exterior algebra of the tangent space. For k = 0, 1, 2 and 3, k-vectors are often called respectively scalars, vectors, bivectors and trivectors; they are respectively dual to 0-forms, 1-forms, 2-forms and 3-forms. (Wikipedia).
Solving a multi-step equation by multiplying by the denominator
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Solving an equation with variables on both side and one solution
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist Solve Multi-Step Equations......Help!
Title: Conley-Morse-Forman theory for generalized combinatorial multivector fields on finite topological spaces Abstract: The combinatorial approach to dynamics has its origins in the Forman's (1998) concept of a combinatorial vector field. The original motivation of Forman was the presen
From playlist ATMCS/AATRN 2020
AGACSE2021 Eric Wieser - Adapting Matrix Algorithms for Multivectors
Adapting Matrix Algorithms for Multivectors. slides at https://eric-wieser.github.io/agacse-2021/
From playlist AGACSE2021
Solving a multi-step equation with fractions and variable on both sides
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
With a variable on both sides solving a multi step equation two ways
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
Solving an equation with fraction where your variable is on both sides
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
AGACSE2021 Anthony Lasenby - Fundamental Forces
Geometric Algebra and the fundamental forces of nature. Slides available at https://bivector.net/A_Lasenby_brno_2021.pdf 00:00 : Characteristic Polynomial 44:27 : The Fundamental Forces
From playlist AGACSE2021
Solving an equation with distributive property on both sides
๐ Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To
From playlist Solve Multi-Step Equations......Help!
Marian Mrozek (8/30/21): Combinatorial vs. Classical Dynamics: Recurrence
The study of combinatorial dynamical systems goes back to the seminal 1998 papers by Robin Forman. The main motivation to study combinatorial dynamics comes from data science. Combinatorial dynamics also provides very concise models of dynamical phenomena. Moreover, some topological invari
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Solve an equation for x by clearing fractions with multiple steps
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
From Zero to Geo Introduction (Geometric Algebra Series)
This video is the introduction to my series on geometric algebra, From Zero to Geo. In this series, we will build geometric algebra from the ground up, starting from just high school algebra. My hope is that this series can be used by motivated high schoolers (or anybody above that level
From playlist From Zero to Geo
Solving an equation with a variable on both sides infinite solutions
๐ Learn how to solve multi-step equations with parenthesis and variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To
From playlist Solve Multi-Step Equations......Help!
Solve an equation with a variable on both sides of the equation
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides
QED Prerequisites Geometric Algebra 5- Multivectors
In this lesson we introduce the idea of multivectors and emphasize the need to understand how to take the spacetime product of any two multivectors in the Spacetime Algebra. We demonstrate how this is done for the product between a vector and a bivector and we interpret the meaning of each
From playlist QED- Prerequisite Topics
Mateus Juda (7/29/20): Unsupervised features learning for sampled vector fields
Title: Unsupervised features learning for sampled vector fields Abstract: In this talk we introduce a new approach to computing hidden features of sampled vector fields. The basic idea is to convert the vector field data to a graph structure and use tools designed for automatic, unsupervi
From playlist AATRN 2020
Geometric Algebra, First Course, Episode 05: Subtraction and Additive Inverse.
We add the ability to compute the additive inverse using unary operator overloading, then implement the subtraction of multivectors, again with binary operator overloading. Addition is also refined as well as defining the ratio of bivectors.
From playlist Geometric Algebra, First Course, in STEMCstudio
QED Prerequisites Geometric Algebra 25 Relative Reversion
In this lesson we learn to use a new partition for a general multivector, a new operation called "relative reversion", and a way to pick apart a multivector to recover the basic quantities of elementary physics. Please consider supporting this channel on Patreon: https://www.patreon.com/
From playlist QED- Prerequisite Topics
A Swift Introduction to Geometric Algebra
This video is an introduction to geometric algebra, a severely underrated mathematical language that can be used to describe almost all of physics. This video was made as a presentation for my lab that I work in. While I had the people there foremost in my mind when making this, I realiz
From playlist Miscellaneous Math
Solving an equation with infinite many solutions 2a+3=3+2a
๐ Learn how to solve multi-step equations with variable on both sides of the equation. An equation is a statement stating that two values are equal. A multi-step equation is an equation which can be solved by applying multiple steps of operations to get to the solution. To solve a multi-s
From playlist How to Solve Multi Step Equations with Variables on Both Sides