gtfitzpatrick said:if the complex vector space is dim 1 then the real part must = 0 so therefore when viewed over R the dimension must be 0 as well
A one dimensional complex space is a vector space over the complex numbers with only one basis vector. This means that any vector in this space can be represented as a linear combination of a single complex number.
A one dimensional complex space has a basis vector that can be multiplied by complex numbers, while a one dimensional real space only allows for multiplication by real numbers. This means that a one dimensional complex space has more degrees of freedom.
One dimensional complex spaces are commonly used in signal processing, specifically in the representation of complex signals. They are also used in quantum mechanics to represent the spin states of particles.
No, a one dimensional complex space cannot be visualized in the traditional sense because it involves complex numbers, which have both a real and imaginary component. However, it can be represented mathematically and can be understood through equations and diagrams.
A one dimensional complex space is a subset of the complex plane, as it only includes vectors with a single basis vector. This means that any vector in a one dimensional complex space can be represented as a point on the complex plane.