All the vector and matrix classes support real and complex element types.
This section discusses some classes specific to complex linear algebra.
Operations Specific to Complex Vectors and Matrices
The complex dot product uses the conjugate of the first argument,
so the dot product of a complex vector with
itself is always a real number.
Complex Vector and Matrix Classes
The ComposedComplexVectorT
class represents a complex vector where the real and imaginary components
are stored as separate vectors. This type permits the efficient representation
of real vectors as complex ones.
For example, because the singular values of a complex matrix are real,
the SingularValues
property of a complex SVD returns a
ComposedComplexVectorT
where the imaginary part is zero.
Likewise, the ComposedComplexMatrixT
class represents a complex matrix where the real and imaginary components
are stored as separate matrices.
A Hermitian matrix is a square, complex matrix that is equal to
its conjugate transpose. Hermitian matrices are similar to real symmetric matrices.
They are discussed in more detail in the section on
Hermitian Matrices.