Question
Prove that the matrix `1/sqrt3` `[[ 1,1+i1],[1-i,-1]]` is unitary.
Solution
Let A= `1/sqrt3[[ 1,1+i],[1-i,-1]]`
The matrix is unitary when A.𝑨𝜽 = 𝑰 .
∴ `A^θ=(\bar{A})^t=1/sqrt3[[ 1,1+i],[1-i,-1]]^t =1/sqrt3[[ 1,1+i],[1-i,-1]]`
∴ `A.A^θ=1/sqrt3[[ 1,1+i],[1-i,-1]]1/sqrt3[[ 1,1+i],[1-i,-1]]`
= `1/3 [[3,0],[0,3]]`
=`[[1,0],[0,1]]`
∴` A.A^θ=I`
The given matrix is unitary is proved.
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APPEARS IN
Solution Prove that the Matrix 1 √ 3 [ 1 1 + I 1 1 − I − 1 ] is Unitary. Concept: .Circular Functions of Complex Number.
