I have a vector space (dim=2) with given basis (x1,x2), and a metric Q=[-1,0;0,1] (Minkowsky metric). Now i perform a transformation on the basis of the form y1=y1(x1,x2), and y2=y2(x1,x2)..the transformation is linear, and the determinat of its matrix is equal to 1.
Does the metric changes?...in that case, how can i find the coeficients of the metric tensor? (coeficients of the matrix)?
Hope i explained myself good enough.
I dont know if i need to specifie more about the transformation. i think to say that its linear, and detT=1 will suffice.
The Attempt at a Solution
I tryed to go to the definition of the components of the metric tenzor...which will satisfy the equation: [Qij=(yi,yj), where the symbol (.,.) means scalar product.
But of course i dont know how tot ake the scalkar product...i mean..should i use the old metric?
Im really lost here..i dont know what to do....
Thx in advance