Coordination System Change Matrix

Let's say we have the default xyz coordination system and want to use the bisectors of the angles of the default coordination system as our new coordination system. What will the transformation Matrix (A) be so that w=A*v, where w,v our old and new systems of coordination respectively

Sorry for syntax errors, but I am not learning math in english, so I am not comfortable with some expressions

Re: Coordination System Change Matrix

Use the following general result: if and are basis of and for , then