If your coordinate system is assumed to be right-handed and given in the following Orthogonal Matrix.
M =[l1 m1 n1;l2 m2 n2;l3 m3 n3]
suppose we multiple this matrix by the following vector v=[a;0;c];
If we multiply the Matrix M with vector v; this will results in a new vector; called:
v_new =[value1; value2;value3].
Can we proof that value1 not equal value2 resulted from the new vector vector_new? Is that possible?
Thanks for the help!
I'm not sure I know what you mean. But let me try to interpret the best way I can:
It depends on the matrix. It's perfeclty possible to get two equal components, if the matrix is just right. You can always find a rotation (orthogonal matrix) that rotates a chosen vector to any direction you want.
Components depend on the choice of your coordinate system anyway, having them equal has no mathematical meaning at all. You can even choose two vector and rotate in such a way that you get the second one to the first one (and you can choose vectors with equal or different components, whatever you want). Just like grabbing a stick and rotating it in the direction you want. No surprise here - rotational matrix rotates stuff.