Matrices¶
Known matrices related to physics
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sympy.physics.matrices.mdft(n)[source]¶ Returns an expression of a discrete Fourier transform as a matrix multiplication. It is an n X n matrix.
Examples
>>> from sympy.physics.matrices import mdft >>> mdft(3) Matrix([ [sqrt(3)/3, sqrt(3)/3, sqrt(3)/3], [sqrt(3)/3, sqrt(3)*exp(-2*I*pi/3)/3, sqrt(3)*exp(-4*I*pi/3)/3], [sqrt(3)/3, sqrt(3)*exp(-4*I*pi/3)/3, sqrt(3)*exp(-8*I*pi/3)/3]])
References
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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:
\(\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3\)
\(\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5\)
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]])
References
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sympy.physics.matrices.msigma(i)[source]¶ Returns a Pauli matrix \(\sigma_i\) with \(i=1,2,3\)
Examples
>>> from sympy.physics.matrices import msigma >>> msigma(1) Matrix([ [0, 1], [1, 0]])
References
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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
To translate a body having a mass of 2 units a distance of 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]])
