The Hadamard matrices H0, H1; H2,... are defined as follows:• H0 is the 1 × 1 matrix [1]•...

The Hadamard matrices H0, H1; H2,... are defined as follows:

• H0 is the 1 × 1 matrix [1]

• For k > 0, Hk is the 2k × 2k matrix

Show that if v is a column vector of length n = 2k, then the matrix-vector product Hkv can be calculated using O (n log n) operations. Assume that all the numbers involved are small enough that basic arithmetic operations like addition and multiplication take unit time.