Question

Which of the following is known as Hadamard matrix?

(a) \(\begin{bmatrix}1 & 0 & 1 & 0\\ 0 & 1 & 0 & 1\\ 1 & 0 & 1 & 0\\ 0 & 1 & 0 & 1\end{bmatrix} \)

(b) \(\begin{bmatrix}1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1 \end{bmatrix} \)

(c) \(\begin{bmatrix}1 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1\\ 1 & 1 & 1 & 1 \end{bmatrix} \)

(d) \(\begin{bmatrix}0 & 0 & 0 & 0\\ 0 & 1 & 1 & 0 \\ 0 & 1 & 1 & 0\\ 0 & 0 & 0 & 0 \end{bmatrix} \)

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Answer 1

Right option is (b) \(\begin{bmatrix}1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1\\ 1 & -1 & 1 & -1 \end{bmatrix} \)

Explanation: Hadamard matrix is named after a famous French mathematician, Jacques Hadamard. It is defined as ‘a square matrix whose entries are only 1 or -1 and whose column (or row) vectors orthogonal’.