Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?

Level: Graduate
Thread starter golekjwb
Start date May 12, 2012
Tags

Determinant Matrix Symmetric Symmetric matrix

Join the discussion

Registration is free. Start your own thread to ask a follow-up.

2 replies · 4K views

golekjwb

Thread starter
May 12, 2012

How to prove that the determinant of a symmetric matrix with the main diagonal elements zero and all other elements positive is not zero and different ?

Physics news on Phys.org

Ultrathin materials could make quantum light circuits programmable
Spin rephasing helps quantum memories store single-photon states longer for future networks
Discovery confirms rare, switchable electrical property in widely used electronics material

Discussion

mathwonk

Science Advisor

Homework Helper

May 13, 2012

different from what?

golekjwb

May 14, 2012

all different element

Is the Determinant of a Symmetric Matrix with Zero Diagonal Elements Non-Zero?

Discussion

Similar threads

Undergrad Non-zero diagonal elements in superconducting qubit transition dipole matrix

Zero-Trace Symmetric Matrix is Orthogonally Similar to A Zero-Diagonal Matrix.

Can a matrix with all zero diagonal entries be diagonalized?

Zero matrix with non-zero above diagonal

Graduate Why are diagonal elements of the imaginary part of a Hermitian matrix zero?

Decompose 4x4 determinant into 24 determinants -- How many are zero?

Graduate Minimize non-zero tiles in symmetric binary matrix via permutation

Undergrad What is the Dimension of the Subspace of M2;2 with Zero Diagonal Entries?

Graduate Why do minors of an n×n matrix with zero row and column sums have equal determinants?

Prove 3x3 Skew symmetric matrix determinant is equal to zero