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Sample examinations Linear Algebra (201-NYC-05) Autumn 2010 1. Given
Sample examinations Linear Algebra (201-NYC-05) Autumn 2010 1. Given

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... Submitted by: Roee Steiner 034744821 Given a spherical shell with radius R and a particle with mass M and charge e. Notice that the standard variables which show the particle are (θ, φ, Lx, Ly, Lz) In this question we have to assume that the particle can be excited from ground state to first energy ...
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LB 220 Homework 1 (due Monday, 01/14/13)

1 Polarization of Light
1 Polarization of Light

... The most general polarization state is |Φi = λ|xi+µ|yi where λ and µ are in general complex with |λ|2 + |µ|2 = 1. Then |Φi is normalized. In the case of linear polarization λ and µ are real and can be written as cos θ and sin θ. The basis states, |xi and |yi, form an orthonormal basis. The state of ...
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Introductory Notes on Vector Spaces

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Orthogonal matrices, SVD, low rank

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BSS 797: Principles of Parallel Computing

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... • From one point of view a vector is just an ordered pair of numbers (x, y). We can associate this vector with the point in R2 which has co-ordinates x and y. We call this vector the position vector of the point. • From the second point of view a vector is a ‘movement’ or translation. For example, t ...
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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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