Orthogonality and Orthonormality
We know that the word orthogonal is kind of like the word perpendicular. It implies that two vectors have an angle of ninety degrees or half pi radians between them. But this term means much more than this, as we can have orthogonal matrices, or entire subspaces that are orthogonal to one
From playlist Mathematics (All Of It)
Orthocenters exist! | Universal Hyperbolic Geometry 10 | NJ Wildberger
In classical hyperbolic geometry, orthocenters of triangles do not in general exist. Here in universal hyperbolic geometry, they do. This is a crucial building block for triangle geometry in this subject. The dual of an orthocenter is called an ortholine---also not seen in classical hyperb
From playlist Universal Hyperbolic Geometry
Math 060 Fall 2017 111317C Orthonormal Bases
Motivation: how to obtain the coordinate vector with respect to a given basis? Definition: orthogonal set. Example. Orthogonal implies linearly independent. Orthonormal sets. Example of an orthonormal set. Definition: orthonormal basis. Properties of orthonormal bases. Example: Fou
From playlist Course 4: Linear Algebra (Fall 2017)
Linear Algebra: Orthonormal Basis
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/ More on unit vectors: https://www.youtube.com/watch?v=C6EYJVBYXIo
From playlist Basics: Linear Algebra
Orthogonal and Orthonormal Sets of Vectors
This video defines orthogonal and orthonormal sets of vectors.
From playlist Orthogonal and Orthonormal Sets of Vectors
Linear Algebra - Lecture 39 - Orthonormal Sets
In this lecture, we discuss orthonormal sets of vectors. We investigate matrices with orthonormal columns. We also define an orthogonal matrix.
From playlist Linear Algebra Lectures
Homomorphisms in abstract algebra
In this video we add some more definition to our toolbox before we go any further in our study into group theory and abstract algebra. The definition at hand is the homomorphism. A homomorphism is a function that maps the elements for one group to another whilst maintaining their structu
From playlist Abstract algebra
Ramanujan Conjecture and the Density Hypothesis - Shai Evra
Joint IAS/Princeton University Number Theory Seminar Topic: Ramanujan Conjecture and the Density Hypothesis Speaker: Shai Evra Affiliation: Princeton University Date: November 19, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Camille Horbez: Measure equivalence and right-angled Artin groups
Given a finite simple graph X, the right-angled Artin group associated to X is defined by the following very simple presentation: it has one generator per vertex of X, and the only relations consist in imposing that two generators corresponding to adjacent vertices commute. We investigate
From playlist Geometry
When invariants are equivalent - Jean Pierre Mutanguha
Short Talks by Postdoctoral Members Topic: When invariants are equivalent Speaker: Jean Pierre Mutanguha Affiliation: Member, School of Mathematics Date: September 28, 2021
From playlist Mathematics
Huaxin Lin: "Non-unital Simple Z-absorbing C*-algebras"
Actions of Tensor Categories on C*-algebras 2021 "Non-unital Simple Z-absorbing C*-algebras" Huaxin Lin - University of Oregon Institute for Pure and Applied Mathematics, UCLA January 26, 2021 For more information: https://www.ipam.ucla.edu/atc2021
From playlist Actions of Tensor Categories on C*-algebras 2021
Complex Analysis: Conformal Automorphisms are Linear!
Today, we prove a theorem that all conformal automorphisms of the complex plane are linear mappings. Casorati Weierstrass Theorem: Part 1 (intro): https://youtu.be/hzZOR-8ETyA Part 2 (proof): https://youtu.be/HfnZrAx5FTo
From playlist Complex Analysis
Math 139 Fourier Analysis Lecture 31: Fourier Analysis on Finite Abelian Groups
Finite abelian groups; characters; dual group. Characters form an orthonormal family: cancellation property (moment condition) of characters; proof of orthonormality; the dual group is an orthonormal basis for the space of functions on the group. Linear algebra: spectral theorem (given a
From playlist Course 8: Fourier Analysis
Louis Funar : Automorphisms of curve and pants complexes in profinite content
Pants complexes of large surfaces were proved to be vigid by Margalit. We will consider convergence completions of curve and pants complexes and show that some weak four of rigidity holds for the latter. Some key tools come from the geometry of Deligne Mumford compactification of moduli sp
From playlist Topology
Non-Vanishing Modulo p of Values of a Modular Form at CM Points (Lecture 2) ) by Haruzo Hida
PROGRAM ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (HYBRID) ORGANIZERS: Ashay Burungale (CalTech/UT Austin, USA), Haruzo Hida (UCLA), Somnath Jha (IIT Kanpur) and Ye Tian (MCM, CAS) DATE: 08 August 2022 to 19 August 2022 VENUE: Ramanujan Lecture Hall and online The program pla
From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)
CTNT 2022 - 100 Years of Chebotarev Density (Lecture 1) - by Keith Conrad
This video is part of a mini-course on "100 Years of Chebotarev Density" that was taught during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - 100 Years of Chebotarev Density (by Keith Conrad)
Title: Interpretations and Differential Galois Extensions
From playlist Fall 2014
Orthonormal bases. The Gram-Schmidt Procedure. Schuur's Theorem on upper-triangular matrix with respect to an orthonormal basis. The Riesz Representation Theorem.
From playlist Linear Algebra Done Right