I'm new to lineair algebra, so maybe I'm asking a stupid question here.
What I mean by title is this command in Matlab / Octave:
v1 = (5 1) sqrt(rotateVector(v1, (deg2rad(90))).^2)
what results (1 5)
I understand this to work only for an initial vector with positive values for its elements.
Is there another way to algebraically switch the elements in a 2D vector, which could also be explained by a geometric operation?
I thought about rotating v1 in 3D around another axis, but that resulted in a vector with twice the number of elements (4 in total).
The reason I'm asking is because I want to understand the dot product geometrically (for 2D vectors). And I look at the relationship to a parallelogram composed of the two vectors or the elements of the two vectors.