Magic squares | Elementary geometry
In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other. For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals. (Wikipedia).
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From playlist Geometry
Geometry - Basic Terminology (23 of 36) Rectangular Solids
Visit http://ilectureonline.com for more math and science lectures! In this video I will define the diagonal of the solid and diagonal of the bottom of a rectangular solid. Next video in the Basic Terminology series can be seen at: http://youtu.be/x4uI-3AePY8
From playlist GEOMETRY 1 - BASIC TERMINOLOGY
Every operator on a finite-dimensional complex vector space has a matrix (with respect to some basis of the vector space) that is a block diagonal matrix, with each block itself an upper-triangular matrix that contains only one eigenvalue on the diagonal.
From playlist Linear Algebra Done Right
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
The Diagonalization of Matrices
This video explains the process of diagonalization of a matrix.
From playlist The Diagonalization of Matrices
Characterizations of Diagonalizability In this video, I define the notion of diagonalizability and show what it has to do with eigenvectors. Check out my Diagonalization playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCSovHY6cXzPMNSuWOwd9wB Subscribe to my channel: https://
From playlist Diagonalization
Determine the length of a diagonal of a rectangle
👉 Learn how to solve problems with rectangles. A rectangle is a parallelogram with each of the angles a right angle. Some of the properties of rectangles are: each pair of opposite sides are equal, each pair of opposite sides are parallel, all the angles are right angles, the diagonals are
From playlist Properties of Rectangles
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of vectors. This video deals with vectors in the 2D and 3D planes, and shows the geometric interpretations of some vector operations. For more math videos, visit our channel or go to www.cen
From playlist Basics: Vectors
Systems of Differential Equations: Diagonalization and Jordan Canonical Form
It is only possible to perfectly diagonalize certain systems of linear differential equations. For the more general cases, it is possible to "block-diagonalize" the system into what is known as Jordan Canonical Form. This video explores these various options and derives the fully general
From playlist Engineering Math: Differential Equations and Dynamical Systems
Georg Biedermann - Higher Sheaves
Talk at the school and conference “Toposes online” (24-30 June 2021): https://aroundtoposes.com/toposesonline/ Joint work with Mathieu Anel, Eric Finster, and André Joyal Even though on the surface the theories look similar, there are basic differences between the classical theory of 1-t
From playlist Toposes online
11. Uncertainty Principle and Compatible Observables (continued)
MIT 8.05 Quantum Physics II, Fall 2013 View the complete course: http://ocw.mit.edu/8-05F13 Instructor: Barton Zwiebach In this lecture, the professor continued to talk about uncertainty principle and compatible observables, etc. License: Creative Commons BY-NC-SA More information at htt
From playlist 8.05 Quantum Physics II - Prof. Barton Zwiebach
Eigenspaces and Diagonal Matrices
Diagonal matrices. Eigenspaces. Conditions equivalent to diagonalizability.
From playlist Linear Algebra Done Right
Totally nonparallel immersions - Michael Harrison
Seminar in Analysis and Geometry Topic: Totally nonparallel immersions Speaker: Michael Harrison Affiliation: Member, School of Mathematics Date: February 08, 2022 An immersion from a smooth n-dimensional manifold M into Rq is called totally nonparallel if, for every pair of distinct poi
From playlist Mathematics
In this video, I define the notion of simultaneous diagonalization and show that two matrices are simultaneously diagonalizable if and only if they commute (that is AB = BA). This is a wonderful exercise using invariant subspaces and diagonalization. Enjoy! Check out my Diagonalization pl
From playlist Diagonalization
String topology and the intersection product - Nathalie Wahl
Members’ Seminar Topic: String topology and the intersection product Speaker: Nathalie Wahl Affiliation: University of Copenhagen; Member, School of Mathematics Date: March 22, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
The Complex Spectral Theorem and the Real Spectral Theorem, with examples.
From playlist Linear Algebra Done Right
A nice basis for a nilpotent operator. Jordan basis. Jordan form for an operator on a finite-dimensional complex vector space.
From playlist Linear Algebra Done Right
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Linear Algebra - Lecture 41 - Diagonalization of Symmetric Matrices
In this lecture, we investigate the diagonalization of symmetric matrices.
From playlist Linear Algebra Lectures