What is the point of all this 20 min of Sal's shit on if change of basis matrix is explained easily in matrix form. Supposing that B is a basis matrix, $\vec v = B [\vec v]_B = BPP^{-1}[\vec v]_B = A[v]_A$, where P is the change of basis matrix sought. Applied to basis B, it produces another basis $A = BP$ and coordinates of v in that basis $[v]_A = P[v]_B$. What is the point of this dull, non-matrix, discussion?

I mean that that we let B to be a basis matrix. Then vector $\vec v = B [\vec v]_B = BPP^{-1}[\vec v]_B = A[v]_A$, where P is the change of basis matrix sought. Applied to basis B, it produces another basis $A = BP$ and coordinates of v in that basis $[v]_A = P[v]_B$. What is the point of this dull, non-matrix, discussion?

What is the point of all this 20 min of Sal's shit on khanacademy.org/math/linear-algebra/alternate_bases/… if change of basis matrix is explained easily in matrix form. And where is the change of basis matrix in his lecture?

Hey guys can you please take a look at my problem- math.stackexchange.com/questions/818982/…