Operations on vectors | Multiplication
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: * Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the magnitudes of the two vectors and the cosine of the angle between the two vectors. Alternatively, it is defined as the product of the projection of the first vector onto the second vector and the magnitude of the second vector. Thus,A ⋅ B = |A| |B| cos θ * More generally, a bilinear product in an algebra over a field. * Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector. The cross product of two vectors in 3-space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle between the two vectors. So, if n̂ is the unit vector perpendicular to the plane determined by vectors A and B,A × B = |A| |B| sin θ n̂ * More generally, a Lie bracket in a Lie algebra. * Hadamard product – entrywise product of vectors, where . * Outer product - where with results in a matrix. * Triple products – products involving three vectors. * Multiple cross products – products involving more than three vectors. (Wikipedia).
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
Linear Algebra for Computer Scientists. 4. Scalar Multiplication of Vectors
This computer science video is the fourth in a series about linear algebra for computer scientists. In this video you will learn how to multiply a vector by a scalar quantity, that is, by a number. You will see that multiplying a vector by a positive scalar results in a new vector with a
From playlist Linear Algebra for Computer Scientists
Vectors: Addition and Scalar Multiplication
This is the first video of a series from the Worldwide Center of Mathematics explaining the basics of vectors. This video deals with vector notation, vector addition, and scalar multiplication. For more math videos, visit our channel or go to www.centerofmath.org
From playlist Basics: Vectors
There are two types of vector multiplication. In this tutorial we take a look at the vector dot product, also known as the vector inner product. The result of a vector inner product is a scalar. There are two ways to calculate this scalar, which can help us to determine the angle betwee
From playlist Introducing linear algebra
Calculus 3: Vector Calculus in 2D (3 of 39) Scalar Multiplication
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain that a scalars only represent magnitude (it has no direction) and can be negative. And I will show how to execute vector scalar multiplication of multiplying a scalar quantity to a vector quan
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
What is a vector? We gently introduce the i and j basis vectors and the idea of a column vector is presented. The algebra of addition, subtraction and scalar multiplication is discussed. Free ebook Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Take a sh
From playlist Introduction to Vectors
Determining if a vector is a linear combination of other vectors
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Determining if a vector is a linear combination of other vectors
From playlist Linear Algebra
Linear Algebra 11c: Definition of Matrix Multiplication for Single Columns on the Right
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
Matrix multiplication. How to multiply matrices. In this video I show you how we define the multiplication of matrices. As you will see, it is not so simply as multiplying two numbers. Matrices can only be multiplied when the number of columns in the first matrix is similar to the numb
From playlist Introducing linear algebra
Lie Groups and Lie Algebras: Lesson 2 - Quaternions
This video is about Lie Groups and Lie Algebras: Lesson 2 - Quaternions We study the algebraic nature of quaternions and cover the ideas of an algebra and a field. Later we will discover how quaternions fit into the description of the classical Lie Groups. NOTE: An astute viewer noted th
From playlist Lie Groups and Lie Algebras
What is a vector space? -- Abstract Linear Algebra 6
⭐Highly Suggested Linear Algebra books⭐ Linear Algebra, an introduction to abstract mathematics: https://amzn.to/3rkp4Wc Linear Algebra Done Right: https://amzn.to/3rkp4Wc The Manga Guide to Linear Algebra: https://amzn.to/3HnS59o A First Course in Linear Algebra: http://linear.ups.edu/ Li
From playlist Abstract Linear Algebra
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras
What is a Tensor? Lesson 20: Algebraic Structures II - Modules to Algebras We complete our survey of the basic algebraic structures that appear in the study of general relativity. Also, we develop the important example of the tensor algebra.
From playlist What is a Tensor?
Unit Vector and Collinear Vectors 2 D
Formula of Unit Vector 00:36 Collinear Vectors defined 2:35 Example 1) 5:29 Example 2) 10:00 Example 3, General Algebraic Coordinates Collinearity Check 17:48 My Vector Lessons nicely organized:) https://www.profrobbob.com/vectors Here are all my Vector lessons: https://www.youtube.com/wat
From playlist Vector Math Lessons
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This series of lecturelets is all about matrix analysis. This first lecture is necessary for all the other ones, because it provides important introductions to what can be done with matrices and vectors, how to scale and multiply them, special kinds of matrices, rank and indendence, and ot
From playlist OLD ANTS #9) Matrix analysis
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Please watch: "UNSWTV: Entertaining your curiosity" https://www.youtube.com/watch?v=bQ7UO8nxiL0 -~-~~-~~~-~~-~- We discuss basic constructions with vectors, and the laws that they satisfy. Affine combinations describe points lying on a line. We give applications to various elementary the
From playlist A first course in Linear Algebra - N J Wildberger
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My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
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In this video, I will introduce general vectorspaces over fields, the dual vectorspace, the cobasis, and general tensors. Translate This Video : http://www.youtube.com/timedtext_video?ref=share&v=1ReUzrT8n_Q Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : ht
From playlist Wrap It Up!
Matrix Multiplication — Topic 19 of Machine Learning Foundations
In this video from my Machine Learning Foundations series, I’ll demonstrate matrix multiplication – the single most important and widely-used mathematical operation in machine learning. To ensure you get a solid grip on the principles of this key skill, we’ll use color diagrams, calculatio
From playlist Linear Algebra for Machine Learning
Motivation for the definition of matrix multiplication. Alternative ways of thinking about matrix multiplication.
From playlist Linear Algebra Done Right
This video introduces the Linear Algebra approach to area, and to volume. It also introduces bi-vectors, with applications from physics: torque, angular momentum and motion in a magnetic field. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning
From playlist A first course in Linear Algebra - N J Wildberger