In relational algebra, a projection is a unary operation written as , where is a relation and are attribute names. Its result is defined as the set obtained when the components of the tuples in are restricted to the set – it discards (or excludes) the other attributes. In practical terms, if a relation is thought of as a table, then projection can be thought of as picking a subset of its columns. For example, if the attributes are (name, age), then projection of the relation {(Alice, 5), (Bob, 8)} onto attribute list (age) yields {5,8} – we have discarded the names, and only know what ages are present. Projections may also modify attribute values. For example, if has attributes , , , where the values of are numbers, thenis like , but with all -values halved. (Wikipedia).
Linear functions -- Elementary Linear Algebra
This lecture is on Elementary Linear Algebra. For more see http://calculus123.com.
From playlist Elementary Linear Algebra
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Proving that orthogonal projections are a form of minimization
Description: Orthogonal projections provide the closest point on a subspace to some point off the subspace. We use Pythagoras to prove that this is always the case. Learning Objective: 1) Given a subspace and a point, compute the closest point in the subspace to the given point. This
From playlist Linear Algebra (Full Course)
11J Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
Geometric Algebra - The Matrix Representation of a Linear Transformation
In this video, we will show how matrices as computational tools may conveniently represent the action of a linear transformation upon a given basis. We will prove that conventional matrix operations, particularly matrix multiplication, conform to the composition of linear transformations.
From playlist Geometric Algebra
Distance in the Coordinate Plane: Conceptual Discovery
Link: https://www.geogebra.org/m/vHyNRbwA
From playlist Algebra 1: Dynamic Interactives!
11I Orthogonal Projection of a Vector
The Orthogonal Projection of one vector along another.
From playlist Linear Algebra
In this tutorial I show a few more notations and share a few more thoughts on mappings.
From playlist Abstract algebra
Chi-Keung Ng: Ortho-sets and Gelfand spectra
Talk by Chi-Keung Ng in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on June 9, 2021
From playlist Global Noncommutative Geometry Seminar (Europe)
Peter McNamara: Hilbert Schemes Appendix (Preprojective Algebras)
SMRI Seminar Series: 'Hilbert Schemes' Appendix (Preprojective Algebras) Peter McNamara (University of Melbourne) Abstract: As mentioned briefly by Tony Licata in his talk, preprojective algebras of affine type appear naturally in the Mackay correspondence. More generally there is a pre
From playlist SMRI Course: Hilbert Schemes
Winter School JTP: From Hall algebras to legendrian skein algebras, Fabian Haiden
A mysterious relation between Hall algebras of Fukaya categories of surfaces and skein algebras was suggested by recent work of Morton-Samuelson and Samuelson-Cooper. I will discuss how this relation can be made precise using knot theory of legendrian curves and general gluing properties o
From playlist Winter School on “Connections between representation Winter School on “Connections between representation theory and geometry"
Gilles de Castro: C*-algebras and Leavitt path algebras for labelled graphs
Talk by Gilles de Castro at Global Noncommutative Geometry Seminar (Americas) on November 19, 2021. https://globalncgseminar.org/talks/tba-16/
From playlist Global Noncommutative Geometry Seminar (Americas)
Representation Theory(Repn Th) 5 by Gerhard Hiss
DATE & TIME 05 November 2016 to 14 November 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore Computational techniques are of great help in dealing with substantial, otherwise intractable examples, possibly leading to further structural insights and the detection of patterns in many abstra
From playlist Group Theory and Computational Methods
Hard Lefschetz Theorem and Hodge-Riemann Relations for Combinatorial Geometries - June Huh
June Huh Princeton University; Veblen Fellow, School of Mathematics November 9, 2015 https://www.math.ias.edu/seminars/abstract?event=47563 A conjecture of Read predicts that the coefficients of the chromatic polynomial of a graph form a log-concave sequence for any graph. A related conj
From playlist Members Seminar
Simon Brain: The Gysin Sequence for Quantum Lens Spaces
This is a joint with Francesca Arici and Giovanni Landi. We construct an analogue of the Gysin sequence for circle bundles, now for q-deformed lens spaces in the sense of Vaksman-Soibelman. Our proof that the sequence is exact relies heavily on the non commutative APS index theory of Care
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
First examples of cluster structures on coordinate algebras,... (Lecture 1) by Maitreyee Kulkarni
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures
Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim
From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory
Reverse Plane Partitions and Modules for the Preprojective Algebra - Anne Dranowski
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Reverse Plane Partitions and Modules for the Preprojective Algebra Speaker: Anne Dranowski Affiliation: Member, School of Mathematics Date: November 19, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Distance in the Coordinate Plane: Interactive, Conceptual Exploration
Distance in the coordinate plane: interactive, conceptual discovery lesson. Create a #GeoGebra class from https://www.geogebra.org/m/urapcmzc & watch your students explore, discover, & reason in real time. #MTBoS #ITeachMath #algebra #geometry
From playlist Algebra 1: Dynamic Interactives!