Let 1 n 1 n be the vector in R n R n whose components are all


Let 1n be the vector in Rn whose components are all one. Show that Jn= 1n1n/n is a projection matrix, i.e., that Jn2=Jn, and that it has rank one: tr(Jn) = 1Extra \left or missing \right. Show also that InJn is the complementary projection of rank n1.

Each of the quadratic forms in Exercise 1.15 can be expressed in the form YMrY, where each Mr is a projection matrix of order mn×mn. Show that each matrix is a Kronecker product

Find the rank of each matrix.

Exercise 1.15

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