Usually a vector is thought of as something with coordinates (x,y,z) meaning (x*e1, y*e2, z*e2) where e1,e2,e3 are orthonormal base vectors.

Here the base vectors e1,e2,e3 change randomly (skew-angular) and the object on the left is the same as on the right except with its points (vectors) being expressed in this new base.

The way these objects behave under a change of basis is a defining property for something being considered a vector (contravariant vector)

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