Hermitian matrix MCQ - Practice Questions & Answers

NIRF Ranking 2024 (Out) - List of Top Engineering Colleges in India

Quick Facts

2 Questions around this concept.

Concepts Covered - 1

Hermitian matrix

Hermitian matrix

A square matrix $\mathrm{A=[a_{ij}]_{n\times n}}$ is said to be Hermitian matrix if $\mathrm{\mathit{a_{ij}=\overline{a_{ji}}}}$ ∀ i, j,

i .e. $\mathrm{A=A^\theta,\;\;[where\;A^\theta\;is\;conjugate\;transpose \;of\;matrix \;A]}$

We know that when we take the transpose of a matrix, its diagonal elements remain the same, and while taking conjugate we just change sign from +ve to -ve and -ve to +ve for imaginary part of all elements, So to satisfy the condition A^? = A diagonal elements must not change, ⇒ all diagonal element must be purely real,

E.g.

$\\\mathrm{Let,\;\;A=\begin{bmatrix} 3 &3-4i & 5+2i\\ 3+4i& 5 &-2+i \\ 5-2i&-2-i &7 \end{bmatrix}}\\\mathrm{Then,}\\\mathrm{\;\;\;\;\;\;\;\;A'=\begin{bmatrix} 3&3+4i &5-2i \\3-4i &5 &-2-i \\ 5+2i & -2+i &7 \end{bmatrix}}\\\\\\\mathrm{\therefore A^\theta=\overline{(A')}=\begin{bmatrix} 3 &3-4i & 5+2i\\ 3+4i& 5 &-2+i \\ 5-2i&-2-i &7 \end{bmatrix}}\\\\\mathrm{here,\;A\;is\;Hermitian\;matrix\;as\;A=A^\theta}$

Note :

For any square matrix say A, with complex number entries,

$\\\mathrm{A+A^\theta \;is \;a\;Hermitian\;matrix}\\\mathrm{[\because (A+A^\theta)^\theta=A^\theta+(A^\theta)^\theta=A^\theta+A]}$

Study it with Videos

Hermitian matrix

Study other Related Concepts

Hermitian matrix Current Topic

Determine The Order Of Matrix

Types of Matrices

Triangular matrix (Upper and Lower triangular matrix)

Matrix operations

Matrix Multiplication

Transpose of a Matrix

Symmetric Matrix & Skew Symmetric Matrix

Conjugate of a Matrix

Hermitian matrix

Skew Hermitian Matrix

"Stay in the loop. Receive exam news, study resources, and expert advice!"

Get Answer to all your questions

JEE Main Articles

JEE Main 2025 Syllabus PDF - Subject-Wise Detailed Syllabus

Sep 16, 2024

JEE Main Physics Syllabus 2025 - Check Topic wise Syllabus PDFs

Sep 16, 2024

JEE Main Registration 2025- IIT Application Form Date, Fees, Documents Required

Sep 16, 2024

10 Common Silly Mistakes to Avoid in IIT JEE 2025

Sep 16, 2024

Most Important Chapters and Topics for JEE Mains 2025 - Tips to Crack, Study Routine

Sep 16, 2024

JEE Main 2025 - Exam Date, Eligibility, Registration, Preparation Tips, Previous Year Papers

Sep 16, 2024

NIT Trichy Cutoff JEE Main 2024- Round Wise BTech Cut Off

Sep 16, 2024

JEE Main Reduced Syllabus 2024 PDF: Deleted Chapters & Topics

Sep 16, 2024

B.Tech/B.Arch Admissions OPEN

Amity University, Noida B.Tech Admissions 2024

Apply

Asia's Only University with the Highest US & UK Accreditation

ITM SLS Baroda University B.Tech Admissions 2024

Apply

Approved by UGC, PCI, & COA. Best Innovative Private Institute in Gujarat. 600+ Recruiters, 3000+ Students Placed, 1500+ Industrial Internship Opportunities, 250+ International Internships.