A Hadamard matrix is a matrix whose entries are all $\backslash$pm $1$ and whose transpose is equal to

its inverse times a constant factor. Show that the following recursive description provides a

Hadamard matrix of each dimension m $=2$k

$,$ k $=0,1,2,...$:

H$0=$

$1$

$,$ Hk$+1=$

Hk Hk

Hk $$Hk