. A Hadamard matrix is a matrix whose entries are all ±1 and whose transpose is equal to its inverse times a constant factor. It is known that if A is a Hadamard matrix of dimension m > 2, then m is a multiple of 4. It is not known, however, whether there is a Hadamard matrix for every such m, though examples have been found for all cases m ~ 424. Show that the following recursive description provides a Hadamard matrix of each dimension m = 2"', k = 0, 1,2, ... : H0 = [ 1 ] ,

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