Section 7.1
... for any choice of real number α. Using the properties of the inner product, this transforms to (x, x) + 2α(x, y ) + α2(y, y ) ≥ 0 This is a quadratic polynomial with respect to the variable α; and it is never negative. Therefore, its discriminant must be non-positive: b2 − 4ac = 4(x, y )2 − 4 (x, x) ...
... for any choice of real number α. Using the properties of the inner product, this transforms to (x, x) + 2α(x, y ) + α2(y, y ) ≥ 0 This is a quadratic polynomial with respect to the variable α; and it is never negative. Therefore, its discriminant must be non-positive: b2 − 4ac = 4(x, y )2 − 4 (x, x) ...