Rotational symmetry | Linear operators | Unitary operators | Euclidean symmetries
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. Rotation can have sign (as in the sign of an angle): a clockwise rotation is a negative magnitude so a counterclockwise turn has a positive magnitude.A rotation is different from other types of motions: translations, which have no fixed points, and (hyperplane) reflections, each of them having an entire (n − 1)-dimensional flat of fixed points in a n-dimensional space. Mathematically, a rotation is a map. All rotations about a fixed point form a group under composition called the rotation group (of a particular space). But in mechanics and, more generally, in physics, this concept is frequently understood as a coordinate transformation (importantly, a transformation of an orthonormal basis), because for any motion of a body there is an inverse transformation which if applied to the frame of reference results in the body being at the same coordinates. For example, in two dimensions rotating a body clockwise about a point keeping the axes fixed is equivalent to rotating the axes counterclockwise about the same point while the body is kept fixed. These two types of rotation are called active and passive transformations. (Wikipedia).
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
ʕ•ᴥ•ʔ Simple Example of Geometry Transformations Rotations
Quickly master rotation symmetry and transformation. Watch more lessons like this and try our practice at https://www.studypug.com/geometry/transformations/rotational-symmetry-and-transformations When an object is turned around its center of rotation to certain degrees and the object loo
From playlist Grade 9 Math (Canada)
What is the difference between rotating clockwise and counter clockwise
👉 Learn how to rotate a figure and different points about a fixed point. Most often that point or rotation will be the original but it is important to understand that it does not always have to be at the origin. When rotating it is also important to understand the direction that you will
From playlist Transformations
Physics, Torque (1 of 13) An Explanation
Explains what torque is, the definition, how it is described and the metric units. Also presented are two examples of how to calculate the torque produced by a force. Torque is a turning force. It is a measure of how much force acting on an object that causes the object to rotate. The ob
From playlist Mechanics
Linear Algebra: Rotation Transformations
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/
From playlist Basics: Linear Algebra
7 Rotation of reference frames
Ever wondered how to derive the rotation matrix for rotating reference frames? In this lecture I show you how to calculate new vector coordinates when rotating a reference frame (Cartesian coordinate system). In addition I look at how easy it is to do using the IPython notebook and SymPy
From playlist Life Science Math: Vectors
Linear Algebra 21i: How to Represent a Rotation with respect to an Arbitrary Axis
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
Transformations on the Number Plane (2 of 2: Rotation & Reflection)
More resources available at www.misterwootube.com
From playlist Basic Linear Relationships
Geometric Algebra - 3D Rotations and Rotors
In this video, we employ the fact that two reflections is a rotation to perform rotations in 3D. We also will derive the general rotation formula, show how to compose rotations, and introduce the rotor version of this formula and discover the rotor's sign flip under a 2pi rotation. Refere
From playlist Math
Elementary Introduction to the Langlands Program, by Edward Frenkel (Part 1) [2015]
"Do we discover mathematics or do we invent it?" One of the most fascinating and important developments in mathematics in the last 50 years is the Langlands Program, a collection of ideas that provides a grand unification of many areas of mathematics. In September 2015, Edward Frenkel g
From playlist Number Theory
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Classes
WSU Master Class: Mathematics, The Language of Nature with Edward Frenkel Course
Join mathematician Edward Frenkel as he discusses how the elegant mathematical formulation of symmetry has been used throughout math and physics and could, through the Langlands program, give rise to a grand unified theory of mathematics. This lecture was recorded on May 31, 2014, at the
From playlist WSU Master Class
LMS Popular Lecture Series 2008, Know your Enemy, Dr Reidun Twarock
LMS Popular Lecture Series 2008, Know your enemy - viruses under the mathematical microscope, Dr Reidun Twarock
From playlist LMS Popular Lectures 2007 - present
Atomistically inspired origami
Oxford Mathematics Public Lectures - Richard James - Atomistically inspired origami The World population is growing at about 80 million per year. As time goes by, there is necessarily less space per person. Perhaps this is why the scientific community seems to be obsessed with folding t
From playlist Oxford Mathematics Public Lectures
Karl Schaffer - Kinesthetic Conundrums - CoM Sept 2021
Karl Schaffer is a dancer/choreographer and mathematician who has co-directed the Dr. Schaffer and Mr. Stern Dance Ensemble with Erik Stern since 1987. Schaffer has written widely on dance and mathematics, and his choreographic work often integrates the two disciplines. His recent concerts
From playlist Celebration of Mind 2021
Mathemalchemy: a mathematical and artistic adventure
This lecture is a visual treat as Ingrid Daubechies celebrates the joy, creativity and beauty of mathematics. Inspired by textile artist Dominique Ehrmann, Ingrid, with Dominique, conceived the idea of a large mathematical installation that incorporated a myriad of mathematical ideas in a
From playlist Oxford Mathematics Public Lectures
Strange Properties of Spinning Black Holes - Kerr Metric, General Relativity, Physics Explained
Hey everyone, I'm back with a video about black holes! This time, we're talking about spinning (rotating) black holes, and their rather interesting characteristics. The mathematical (and theoretical) properties of a rotating black hole are described by the Kerr metric. This metric is a s
From playlist Relativity by Parth G
Advanced Quantum Mechanics Lecture 5
(October 21, 2013) Leonard Susskind introduces the spin statistics of Fermions and Bosons, and shows that a single complete rotation of a Fermion is not an identity operation, but rather induces a phase change that is detectable. Originally presented by the Stanford Continuing Studies Pro
From playlist Lecture Collection | Advanced Quantum Mechanics
8ECM Public Lecture: Andrei Okounkov
From playlist 8ECM Public Lectures
Physics 11.1 Rigid Body Rotation (1 of 10) Basics
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the translational, rotational, and combined motion of rigid body rotation.
From playlist PHYSICS 11 ROTATIONAL MOTION