(1, -3)^{T} **·** (1, -3)^{T} = (1)(1) + (-3)(-3) = 1 + 9 = 10

As with vectors, the dot product of a column matrix with itself will always be positive.

(x, y, z)^{T}·(x, y, z)^{T}= x^{2}+ y^{2}+ z^{2}= something zero or positive

No matter what x, y, and z are, their square is going to be zero or greater. So the sum is going to be zero or greater.

The only time the square of a real number is zero is when the real number is zero; so the only time the dot product of a column matrix with itself is zero is when it is the zero column matrix.