Inner Product Spaces

Abstract

Up to now we have considered vector spaces over arbitrary fields. In this chapter we will restrict ourselves to vector spaces over M or C. Recall that if z-a + bi G C then z = a-bi. In particular, if a ∈ ℝ then ā = a. If A = [a_ij] ∈ ℳ_n×n(ℂ) then we define the conjugate transpose A of A to be the matrix [b_ij], where b_ij = ā_ji for all 1 ≤ i,j ≤ n.