Question

I was reading gradient in a book and I came across a line saying gradient has length and directon independent of the choice of cartesian coordinates. How...?

Answer 1

Gradient VECTOR field. If it is a vector that would make sense

Answer 2

Length/magnitude YES, direction NO. The direction will be independent of co-ordinates which differ by translation and equal scaling of the axes, BUT it will NOT be independent of rotational transformations.