Welcome! You have found the homepage of the Spring 2025 manifestation of Math 781.
In sage, the variables i and I can be used
interchangably as the "imaginary unit".
The commands z.real() and z.imag() calculate the
real and imaginary parts of z. The
commands z.conjugate() and z.abs() calculate the
conjugate and absolute value of z. We can calculate the
recriprocal of z with 1/z.
Of course, we can add and multiply complex numbers with the
syntax z1+z2 and z1*z2.
We can use the expected syntax to define a complex matrix A and
a complex vector v. The syntax A*v calculates the
associated matrix-vector product. The conjugate-transpose of A
is given by A.H.
The inner product of two complex vectors is given
by v1.hermitian_inner_product(v2).