A complex vector space is a mathematical structure formed by vectors that can be scaled by complex numbers. These vectors can be added together and multiplied by complex numbers, following specific rules. The space is defined over the field of complex numbers, which includes real numbers and imaginary numbers, allowing for a richer set of operations compared to real vector spaces. In a complex vector space, concepts like linear independence, basis, and dimension still apply, similar to real vector spaces. An important example of a complex vector space is the space of complex numbers themselves, often denoted as ℂ. This framework is essential in various fields, including quantum mechanics and signal processing.