ST259 Lecture : 6.1 — Inner Products and Norms
Document Summary
Defalet aemmm f wedefinetheconjugatetranspose or adjoint of a to bethe nxm matrix a suchthat ca i atfor all i j. Avectorspace v over f endowed with a specificinner product iscalled an inner productspace. If f c we call v a complex inner product space whereas if f r we call v a real productspace. It is clearthat if v has an inner product soxy and w is a subspace of v then w is also an inner productspace whenthe same function x y is restricted tothevectors x ycw. Tha6 iiet v be an inner productspace thenfor x y zev and cef thefollowing statements are true x y iz. Defatet v be an innerproductspace forxev we definethe norm or length of oxby1h11 ried. Tha6. 2let v be an innerproductspaceoverfthenforall xyellandcef thefollowing statements are true. 11 11 0 iff x o inanycase 11 1130. Cauchy schwarzinequality k x y i e11 11 hyll.
