A matrix with diagonal elements as complex numbers with imaginary part not 0 can never be Hermitian matrix

True

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

False

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
True

Lets take general element from matrix A aij

Assume

aij = p + iq

If aij is a diagonal element then i=j. So if we take the conjugate of this element it will be p-iq which is not equal to p+iq. Therefore matrices with diagonal elements as complex number with imaginary part not 0 can’t be hermitian matrices.

Suggest Corrections

Similar questions

A^{*}

a_{i j}

\frac{A + A^{*}}{2} .

A^{*}

a_{i j}

\frac{A + A^{*}}{2} .

A Hermitian matrix is a square matrix with complex entries that is equal to its own conjugate.

A Matrix of any order can be a hermitian matrix

In a square matrix of order 4, the element $a_{33}$ = 33. This square matrix cannot be skew hermitian.

Join BYJU'S Learning Program