pseudovectorial

Pseudovectorial refers to a concept in mathematics and physics that describes quantities possessing both magnitude and direction, but which transform differently under a parity transformation compared to true vectors. While true vectors reverse their direction when the coordinate system is inverted (e.g., a velocity vector pointing right will point left if you invert the x-axis), pseudovectors do not. Instead, they either retain their direction or transform in a more complex way that depends on the dimensionality of the space.

This distinction is crucial in fields like electromagnetism and quantum mechanics. For example, the magnetic field is a pseudovector. If you were to flip the sign of all coordinates in your system, the magnetic field vector would not simply reverse its direction as a true vector would. Other examples of pseudovectors include angular momentum and the cross product of two true vectors. The term "pseudovector" is sometimes used interchangeably with "axial vector" or "curl vector," though subtle differences in definition can exist depending on the specific mathematical context. Understanding the difference between vectors and pseudovectors is essential for correctly applying physical laws and interpreting experimental results, particularly when dealing with symmetry operations.