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( 2 0 points ) Assume that n is a power of two. The Hadamard matrix Hn is defined as follows: H 1 = 1

(20 points) Assume that n is a power of two. The Hadamard matrix Hn is defined as follows:
H1=
1
H2=
11
11
Hn =
Hn/2 Hn/2
Hn/2Hn/2
Design an O(n log n) algorithm that calculates the vector Hnv, where n is a power of 2 and v is a
vector of length n. Justify the runtime of your algorithm by providing a recurrence relation and
solving it.(Hint: you may assume adding two vectors of order n takes O(n) time.)

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