How do I prove that dot product of two free vectors ( inner product in 2D and 3D vectors) does not depend on the choice of frames in which their coordinates are defined?
Inner product and the choice of coordinate frames
2
$\begingroup$
linear-algebra
inner-product-space
-
01) What do you mean by a "frame" ? 2) What do you mean by a "dot" product? – 2011-02-03
-
0frame = basis (it's a more physical terminology) and dot product is scalar product. – 2011-02-03
-
0You should state what definition of dot product you are using. – 2011-02-03
-
03) What do you mean by a 'free vector'? – 2011-02-03
-
0probably linearly independent, and frame probably means orthonormal basis. – 2011-02-03
-
0Because the dot product is defined in a coordinate-independent fashion: $\mathbf x \cdot \mathbf y = |\mathbf x| |\mathbf y|\cos\left(\angle\mathbf x\mathbf y\right)$. – 2011-02-03