Applet : Coordinates with Respect to Change of Basis

Let be any basis of . Let be its coordinates with respect to standard basis , where . Let v has coordinates with respect to basis .

If , then

This gives unique value of , .

How to Use this Applet :

In this Applet, default values of vector , and are  (-1,1) , (2,3) and (-1,-1) are given respectively. You can   enter values for , , and click OK to see the  values of and . You can also change the values of , and by selecting the scroll bar and using the sliders for X - axis and Y - axis at the bottom.


By solving these two equations we can find the value of and .
It's values are and