You need to be more clear. None of v1
, v2
, or M
have any alpha or beta in them, so I can't tell how you got that result.
As for "clearly equivalent", no they are clearly NOT equivalent. There is an extra List layer in the first element of the left hand side.
If I follow your definition, I get this:
v1 = {u, v, w};
v2 = {x, y};
M = {{a, a}, {b, b}, {-c, c}};
v1 == M . v2
{u, v, w} == {a x + a y, b x + b y, -c x + c y}
So, there is no way it can determine equality.