In this video, I define a cool operation called the symmetrization, which turns any matrix into a symmetric matrix. Along the way, I also explain how to show that an (abstract) linear transformation is one-to-one and onto. Finally, I show how to decompose and matrix in a nice way, sort of
From playlist Linear Transformations
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Linear Algebra: Continuing with function properties of linear transformations, we recall the definition of an onto function and give a rule for onto linear transformations.
From playlist MathDoctorBob: Linear Algebra I: From Linear Equations to Eigenspaces | CosmoLearning.org Mathematics
What is an enlargement dilation
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
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
Polarization of Light: circularly polarized, linearly polarized, unpolarized light.
3D animations explaining circularly polarized, linearly polarized, and unpolarized electromagnetic waves.
From playlist Physics
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Which Complete Graphs are Planar? | Graph Theory
Which complete graphs are planar? Which complete graphs are nonplanar? We'll answer this question in today's graph theory lesson! We'll see that K1, K2, K3, and K4 are all planar complete graphs. Then, we'll prove that K5 is nonplanar and see why that implies no complete graph with at le
From playlist Graph Theory
A Classification of Planar Graphs - A Proof of Kuratowski's Theorem
A visually explained proof of Kuratowski's theorem, an interesting, important and useful result classifying "planar" graphs. Proof adapted from: http://math.uchicago.edu/~may/REU2017/REUPapers/Xu,Yifan.pdf and: https://www.math.cmu.edu/~mradclif/teaching/228F16/Kuratowski.pdf Also check
From playlist Summer of Math Exposition Youtube Videos
This is Lecture 22 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2022.pdf More information may
From playlist CSE547 - Discrete Mathematics - 1999 SBU
Graph Theory: 61. Characterization of Planar Graphs
We have seen in a previous video that K5 and K3,3 are non-planar. In this video we define an elementary subdivision of a graph, as well as a subdivision of a graph. We then discuss the fact that if a graph G contains a subgraph which is a subdivision of a non-planar graph, then G is non-
From playlist Graph Theory part-10
What are Planar Graphs? | Graph Theory
What are planar graphs? How can we draw them in the plane? In today's graph theory lesson we'll be defining planar graphs, plane graphs, regions of plane graphs, boundaries of regions of plane graphs, and introducing Euler's formula for connected plane graphs. A planar graph is a graph t
From playlist Graph Theory
From playlist Plenary talks One World Symposium 2020
[Discrete Mathematics] Planar Graphs
We look at planar graphs and how to determine if a graph is planar or not. Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW *--Playlists--* Discrete Mathematics 1: https://www.youtube.com/playlist?list=PLDDGPdw7e6Ag1EIznZ-m-qXu4XX3A0cIz Discrete Mathem
From playlist Discrete Math 2
Due to the COVID-19 pandemic, Carnegie Mellon University is protecting the health and safety of its community by holding all large classes online. People from outside Carnegie Mellon University are welcome to tune in to see how the class is taught, but unfortunately Prof. Loh will not be o
From playlist CMU 21-228 Discrete Mathematics
Featuring Professor Maria Chudnovsky from Princeton University - see part two about her work on Perfect Graphs - https://youtu.be/C4Zr4cOVm9g More links & stuff in full description below ↓↓↓ Correction at 13:58 - remove the word "not". Professor Chudnovsky's webpage: https://web.math.pri
From playlist Women in Mathematics - Numberphile
This video introduces the concept of phased arrays. An array refers to multiple sensors, arranged in some configuration, that act together to produce a desired sensor pattern. With a phased array, we can electronically steer that pattern without having to physically move the array simply b
From playlist Understanding Phased Array Systems and Beamforming
Graph Theory: 60. Non Planar Graphs
In this video we formally prove that the complete graph on 5 vertices is non-planar. Then we prove that a planar graph with no triangles has at most 2n-4 edges, where n is the number of vertices. Using this fact, we formally prove that the complete biparite graph with partite sets both o
From playlist Graph Theory part-10