In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from angle to angle" (from διά- dia-, "through", "across" and γωνία gonia, "angle", related to gony "knee"); it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as diagonus ("slanting line"). In matrix algebra, the diagonal of a square matrix consists of the entries on the line from the top left corner to the bottom right corner. There are also other, non-mathematical uses. (Wikipedia).
The Diagonalization of Matrices
This video explains the process of diagonalization of a matrix.
From playlist The Diagonalization of Matrices
This video defines a diagonal matrix and then explains how to determine the inverse of a diagonal matrix (if possible) and how to raise a diagonal matrix to a power. Site: mathispower4u.com Blog: mathispower4u.wordpress.com
From playlist Introduction to Matrices and Matrix Operations
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
Diagonal Matrices are Freaking Awesome
When you have a diagonal matrix, everything in linear algebra is easy Learning Objectives: 1) Solve systems, compute eigenvalues, etc for Diagonal Matrices This video is part of a Linear Algebra course taught by Dr. Trefor Bazett at the University of Cincinnati
From playlist Linear Algebra (Full Course)
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
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
Number of Diagonals in a Polygon
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From playlist Geometry
What are the Angle Relationships for Parallel Lines and a Transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
What are parallel lines and a transversal
👉 Learn about converse theorems of parallel lines and a transversal. Two lines are said to be parallel when they have the same slope and are drawn straight to each other such that they cannot meet. In geometry, parallel lines are identified by two arrow heads or two small lines indicated i
From playlist Parallel Lines and a Transversal
2013 AMC 10 A #25 | AMC 10 | Math for fun and glory | Khan Academy
Video by Art of Problem Solving. Problem from the MAA American Mathematics Competitions. Created by Art of Problem Solving. Watch the next lesson: https://www.khanacademy.org/math/math-for-fun-and-glory/aime/2003-aime/v/2003-aime-ii-problem-1?utm_source=YT&utm_medium=Desc&utm_campaign=ma
From playlist AMC 10 | Math for fun and glory | Khan Academy
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
Diagonals of Rational Functions Diagonals of rational functions naturally occur in many applications, study several families of rational functions in three or four variables and investigate the nature of their diagonals (hypergeometric 2F1 functions, Heun functions, modular forms, functi
From playlist DART X
Polynomials, Matrices and Pascal Arrays | Algebraic Calculus One | Wild Egg
We introduce some basic orientation towards polynomials and matrices in the context of the Pascal-type arrays that figured in our analysis of the Faulhaber polynomials and Bernoulli numbers in the previous video. The key is to observe some beautiful factorizations that occur involving diag
From playlist Algebraic Calculus One from Wild Egg
The Sudoku With Only 6 Given Digits
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From playlist Aad Van De Wetering Puzzles
Does This Sudoku Have Invisible Digits?!
Aad van de Wetering's latest sudoku scrambles Simon's brain to the extent that he appears unable to see the number 9! Play the puzzle here: https://cracking-the-cryptic.web.app/sudoku/dN6dFnnLGq Rules: Normal sudoku rules apply. In addition each of the four marked 8-cell diagonals mu
From playlist Aad Van De Wetering Puzzles
A friendly introduction to Convolutional Neural Networks and Image Recognition
Announcement: New Book by Luis Serrano! Grokking Machine Learning. bit.ly/grokkingML 40% discount code: serranoyt A friendly explanation of how computer recognize images, based on Convolutional Neural Networks. All the math required is knowing how to add and subtract 1's. (Bonus if you kn
From playlist Neural Networks
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