Question: Let 1 ,,k be positive numbers adding to unity and define the multinomial covariance matrix ij = { . Show that ij has rank k

Let π1

,…,πk be positive numbers adding to unity and define the multinomial covariance matrix

ωij = { .

Show that ωij has rank k − 1 and that is a generalized inverse of rank k. Find the Moore-Penrose generalized inverse.

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