Matrices

Known matrices related to physics

sympy.physics.matrices.mdft(n)

Returns an expression of a discrete Fourier transform as a matrix multiplication. It is an n X n matrix.

References

[R402]

https://en.wikipedia.org/wiki/DFT_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]])

sympy.physics.matrices.mgamma(mu, lower=False)

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:

\(\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3\)

\(\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5\)

References

[R403]

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]])

sympy.physics.matrices.msigma(i)

Returns a Pauli matrix \(\sigma_i\) with \(i=1,2,3\)

References

[R404]

http://en.wikipedia.org/wiki/Pauli_matrices

Examples

>>> from sympy.physics.matrices import msigma
>>> msigma(1)
Matrix([
[0, 1],
[1, 0]])

sympy.physics.matrices.pat_matrix(m, dx, dy, dz)

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]])