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# Matrices¶

Known matrices related to physics

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.

References

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)[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:

$$\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3$$

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

References

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)[source]

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

References

Examples

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

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]])


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