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Dynamics
Dynamics

On the Essence of Electric Charge
On the Essence of Electric Charge

... entity. Physicists have different, sometimes conflicting, ideas about the physical meaning of the mathematical objects in their models. The mathematical objects of General Relativity, as an example, are n-dimensional manifolds in hyper-spaces with more dimensions than n. These are not necessarily th ...
Matrices
Matrices

the jordan normal form
the jordan normal form

Matrix Methods for Field Problems
Matrix Methods for Field Problems

Sketching as a Tool for Numerical Linear Algebra
Sketching as a Tool for Numerical Linear Algebra

DX25751756
DX25751756

... recognition. A common way to attempt to resolve this problem is to use dimension reduction techniques. In order to reduce the feature vector dimension and increase the discriminative power, the principal component analysis (PCA) has been used. In these approaches, the 2-dimensional image is consider ...
Matrices with a strictly dominant eigenvalue
Matrices with a strictly dominant eigenvalue

Homework - Exam From last time… Time dilation, length contraction
Homework - Exam From last time… Time dilation, length contraction

... • Views of the same cube from two different angles. • Distance between corners (length of red line drawn on the flat page) seems to be different depending on how we look at it. ...
2. HARMONIC ANALYSIS ON COMPACT
2. HARMONIC ANALYSIS ON COMPACT

Part I - Otterbein
Part I - Otterbein

sobol1
sobol1

form Given matrix The determinant is indicated by
form Given matrix The determinant is indicated by

... What is a DETERMINANT? ▪ The determinant of a matrix is a NUMBER that is associated to that matrix that helps us to determine things about that matrix. ▪ Only SQUARE matrices have determinants. ▪ You will be required to find determinants of 2x2 and 3x3 determinants by hand. ...
Fast-Fourier Optimization
Fast-Fourier Optimization

Rank (in linear algebra)
Rank (in linear algebra)

4. SYSTEMS OF LINEAR EQUATIONS §4.1. Linear Equations
4. SYSTEMS OF LINEAR EQUATIONS §4.1. Linear Equations

... When a system of equations is solved by a computer program the coefficients and constants are stored in an array. There needs to be some systematic algorithm, or procedure. The three types of operation carried out by such a program are: • Dividing a row of the augmented matrix by a non-zero constant ...
Gravitoelectromagnetism (GEM): A Group
Gravitoelectromagnetism (GEM): A Group

linear transformations and matrices
linear transformations and matrices

Vectors and Scalars - The Physics Teacher
Vectors and Scalars - The Physics Teacher

5 Unitary groups
5 Unitary groups

Physics 108
Physics 108

Lagrangian and Hamiltonian Dynamics
Lagrangian and Hamiltonian Dynamics

Backtracking and Branch and Bound
Backtracking and Branch and Bound

Sequences and Convergence in Metric Spaces
Sequences and Convergence in Metric Spaces

Modern Physics Notes
Modern Physics Notes

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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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