Linear Algebra: Transition Matrix

This videos explains how to find a transition matrix which translates coordinate vectors from a basis to a new basis in Euclidean vector spaces.

[maxpercer]

Here is a little theory to go along with your example.
Define [x]_A to be the coordinate vector of x with respect to the ordered basis A.
The standard ordered basis for R^3 are the column vectors, typed out horizontally, { (1, 0, 0 ), (0, 1, 0), (0, 0, 1) } .
Let U be the row matrix of basis (column) vectors [ u1 u2 u3 ],
and W be the row matrix of basis (column) vectors [ w1 w2 w3 ] .
Then U . [x]_U = x, and W . [x]_W = x.
By substitution, since both LHS (left hand side) terms are equal to the vector x,
U . [x]_U = W . [x]_W .
Multiplying both sides of the latter equation by W ^-1, we get
W^-1 . U . [x]_U = [x] _W.

[christianlauridsen]

Nice video VietMath :) made it really simple :D