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1.2 Single Particle Kinematics
1.2 Single Particle Kinematics

... has no physical significance unless it has been choosen in some physically meaningful way. In general the multiplication of a position vector by a scalar is as meaningless physically as saying that 42nd street is three times 14th street. The cartesian components of the vector ~r, with respect to som ...
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Classical Electrodynamics - Duke Physics

The Inverse of a Square Matrix
The Inverse of a Square Matrix

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Invertible matrix

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Classical Electrodynamics - Duke Physics

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Math 427 Introduction to Dynamical Systems Winter 2012 Lecture

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... are all unit vectors. A vector whose i th element is one and the remaining elements are all zero is called the i th Cartesian unit vector. Let θ denote the angle between y and z. By the law of cosine, y − z2 = y2 + z2 − 2y z cos θ, where the left-hand side is y2 + z2 − 2y  z. Thus, th ...
6.1 Orientation
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SOME QUESTIONS ABOUT SEMISIMPLE LIE GROUPS
SOME QUESTIONS ABOUT SEMISIMPLE LIE GROUPS

... In this paper we consider some interesting well known facts from Matrix Theory and try to generalize them to arbitrary semisimple complex Lie groups. For instance, it is known that every n by n complex matrix x with zero trace is unitarily similar to a matrix with zero diagonal. We can view x as an ...
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The most basic introduction to mechanics requires vector concepts

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Matrix Manipulation and 2D Plotting

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611: Electromagnetic Theory II

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Finding the Inverse of a Matrix

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Conservation of Linear Momentum Solutions

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Studia Seientiaruin Mathematicarum Hungarica 3 (1968) 459

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Semidefinite and Second Order Cone Programming Seminar Fall 2001 Lecture 9

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On the nature of the photon and the electron

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THE DIRAC OPERATOR 1. First properties 1.1. Definition. Let X be a

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Differential Equations and Linear Algebra 2250-10 7:15am on 6 May 2015 Instructions

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CHAPTER 4: PRINCIPAL BUNDLES 4.1 Lie groups A Lie group is a

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Four-vector

In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.
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