I can’t understand at all this topic, that we should use in assigment.

Why here, for example, we see, that rotation appears, if we use negative number by y axis in first eigenvector?

And I a bit not understand what means 1 and 0 in eginvectors at all? I thought that 0 means, that value of this axis after transformation should be zero and if 1 — value should be the same, as initially by this axis, isn’t it?

So, why sheer works? Ok, we keep unchanged horizontal vector. But why 0 in x axis of eigenvector should transform vertical line in the way when its second point will be on the same level by X axis as second point of horizontal vector? We just multilpied on 0. If I understand correct, we should see 0 by x axis too after multiplication, isn’t it?