In mathematics, an affine combination of x1, ..., xn is a linear combination such that Here, x1, ..., xn can be elements (vectors) of a vector space over a field K, and the coefficients are elements of K. The elements x1, ..., xn can also be points of a Euclidean space, and, more generally, of an affine space over a field K. In this case the are elements of K (or for a Euclidean space), and the affine combination is also a point. See Affine space § Affine combinations and barycenter for the definition in this case. This concept is fundamental in Euclidean geometry and affine geometry, because the set of all affine combinations of a set of points forms the smallest subspace containing the points, exactly as the linear combinations of a set of vectors form their linear span. The affine combinations commute with any affine transformation T in the sense that In particular, any affine combination of the fixed points of a given affine transformation is also a fixed point of , so the set of fixed points of forms an affine subspace (in 3D: a line or a plane, and the trivial cases, a point or the whole space). When a stochastic matrix, A, acts on a column vector, b→, the result is a column vector whose entries are affine combinations of b→ with coefficients from the rows in A. (Wikipedia).
Combination Locks - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Make A Combination Lock - Intro to Algorithms
This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.
From playlist Introduction to Algorithms
Types of Matrices and Matrix Addition
Alright, so we know what matrices are and we can use them to solve systems of linear equations, but we also have to do algebra with them! Let's start with the simplest operation of all, let's learn how to add two matrices together. Watch the whole Mathematics playlist: http://bit.ly/ProfD
From playlist Mathematics (All Of It)
C07 Homogeneous linear differential equations with constant coefficients
An explanation of the method that will be used to solve for higher-order, linear, homogeneous ODE's with constant coefficients. Using the auxiliary equation and its roots.
From playlist Differential Equations
Linear Algebra for Computer Scientists. 7. Linear Combinations of Vectors
This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about linear combinations of vectors, that is, you will learn how to create new vectors by scaling then adding other vectors together. You will also learn that some sets
From playlist Linear Algebra for Computer Scientists
Linear Algebra for Computer Scientists. 8. Convex Combinations of Vectors
This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about convex combinations of vectors. A convex combination is a special type of linear combination, in which the coefficients must add up to one, and are both greater tha
From playlist Linear Algebra for Computer Scientists
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From playlist Algebra II
Ex: Evaluate a Combination and a Permutation - (n,r)
This video explains how to evaluate a combination and a permutation with the same value of n and r. Site: http://mathispower4u.com
From playlist Permutations and Combinations
Novel Algebraic Operations for Affine Geometry | Algebraic Calculus One | Wild Egg
We introduce some novel conventions to help us set up the foundations of affine geometry. We learn about differences of points, sums of points and vectors, affine combinations and vector proportions. And then use these to state a number of important results from affine geometry, including
From playlist Algebraic Calculus One from Wild Egg
Affine Combinations and Barycentric Coords | Algebraic Calculus One | Wild Egg
In this video we show how affine combinations and barycentric coordinates express mathematically what Archimedes' Law of the Lever captures in terms of the centre of mass of a triangle. We examine both the one dimensional case of a segment, as well as the more general two dimensional case
From playlist Algebraic Calculus One from Wild Egg
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 7 - VMLS linear functions
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares
Robert Cass: Perverse mod p sheaves on the affine Grassmannian
28 September 2021 Abstract: The geometric Satake equivalence relates representations of a reductive group to perverse sheaves on an affine Grassmannian. Depending on the intended application, there are several versions of this equivalence for different sheaf theories and versions of the a
From playlist Representation theory's hidden motives (SMRI & Uni of Münster)
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 23-VMLS vector linear func
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares
The One Dimensional Random Walk Hypergroup | Diffusion Symmetry 6 | N J Wildberger
We introduce affine transformations, in the form of the ax+b group, to describe the classical (group theoretic) symmetries of the simplest lattice - the one dimensional integral lattice. We meet the fundamental idea of representation theory: assigning concrete matrices to abstract algebrai
From playlist Diffusion Symmetry: A bridge between mathematics and physics
Chemistry - Periodic Variations (21 of 23) Electron Affinity and the Second Electron
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the electron affinity and the second electron.
From playlist CHEMISTRY 12 PERIODIC VARIATION
WildLinAlg3: Center of mass and barycentric coordinates
Please watch: "UNSWTV: Entertaining your curiosity" https://www.youtube.com/watch?v=bQ7UO8nxiL0 -~-~~-~~~-~~-~- This video introduces several important applications of vectors. First we review the connections with force, velocity and acceleration, and introduce some games. Then we study
From playlist A first course in Linear Algebra - N J Wildberger
WildLinAlg1: Introduction to Linear Algebra
Please watch: "UNSWTV: Entertaining your curiosity" https://www.youtube.com/watch?v=bQ7UO8nxiL0 -~-~~-~~~-~~-~- The first of a series of lectures on Linear Algebra meant for freshman university students. This course emphasizes the geometric content of the subject, along with applications
From playlist A first course in Linear Algebra - N J Wildberger
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From playlist Chemistry
A Level Biology Revision "Haemoglobin and the Oxygen Dissociation Curve"
In this video, we look at the role of haemoglobin in transporting oxygen. First we explore how erythrocytes (red blood cells) are adapted for oxygen transport. We then look at the structure of haemoglobin and how haemoglobin binds reversibly to oxygen. Finally, we explore the oxygen dissoc
From playlist A Level Biology "Exchange and Transport in Animals"