Matrices¶
Known matrices related to physics
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sympy.physics.matrices.
mgamma
(mu, lower=False)[source]¶ Returns a Dirac gamma matrix gamma^mu in the standard (Dirac) representation.
If you want gamma_mu, use gamma(mu, True).
We use a convention:
gamma^5 = I * gamma^0 * gamma^1 * gamma^2 * gamma^3 gamma_5 = I * gamma_0 * gamma_1 * gamma_2 * gamma_3 = - gamma^5
References
[R222] http://en.wikipedia.org/wiki/Gamma_matrices Examples
>>> from sympy.physics.matrices import mgamma >>> mgamma(1) Matrix([ [ 0, 0, 0, 1], [ 0, 0, 1, 0], [ 0, -1, 0, 0], [-1, 0, 0, 0]])
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sympy.physics.matrices.
msigma
(i)[source]¶ Returns a Pauli matrix sigma_i. i=1,2,3
References
[R223] http://en.wikipedia.org/wiki/Pauli_matrices Examples
>>> from sympy.physics.matrices import msigma >>> msigma(1) Matrix([ [0, 1], [1, 0]])
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sympy.physics.matrices.
pat_matrix
(m, dx, dy, dz)[source]¶ Returns the Parallel Axis Theorem matrix to translate the inertia matrix a distance of (dx, dy, dz) for a body of mass m.
Examples
If the point we want the inertia about is a distance of 2 units of length and 1 unit along the x-axis we get: >>> from sympy.physics.matrices import pat_matrix >>> pat_matrix(2,1,0,0) Matrix([ [0, 0, 0], [0, 2, 0], [0, 0, 2]])
In case we want to find the inertia along a vector of (1,1,1): >>> pat_matrix(2,1,1,1) Matrix([ [ 4, -2, -2], [-2, 4, -2], [-2, -2, 4]])