What is the minimum rank of a skew symmetric matrix?

Click For Summary

Discussion Overview

The discussion centers on the properties of skew symmetric matrices, specifically focusing on the minimum and maximum possible ranks of such matrices. Participants explore theoretical implications and definitions related to skew symmetric matrices.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the minimum possible rank of a skew symmetric matrix.
  • Another participant suggests that the zero matrix serves as an example of a skew symmetric matrix.
  • A subsequent reply challenges the classification of the zero matrix as skew symmetric, prompting a clarification that the zero matrix satisfies the condition for skew symmetry.
  • Another participant introduces a related question regarding the maximum rank of a 3x3 skew symmetric matrix.
  • It is noted that the determinant of a skew symmetric matrix of odd order is always zero, leading to the assertion that the rank of such matrices must be even.

Areas of Agreement / Disagreement

Participants express differing views on the minimum rank of skew symmetric matrices, with some asserting the zero matrix as an example, while others question this classification. The discussion on maximum rank introduces additional complexity, indicating that multiple competing views remain.

Contextual Notes

The discussion does not resolve the assumptions regarding the definitions of rank and skew symmetry, nor does it clarify the implications of the determinant condition on rank.

bhanesh
Messages
9
Reaction score
0
What is minimum possible rank of skew symmetric matrix ?
 
Physics news on Phys.org
Look at the zero matrix.
 
But how can we say that zero matrix is skew symmetric matrix
 
If 0 denotes the zero matrix, then 0T + 0 = 0. So this matrix is skew-symmetric.
 
a little more surprising question might be what is the maximum rank, say of a 3by3 skew symmetric matrix?
 
Determinant of skew symmetric matrix of odd order is always zero. So for skew symmetric matrix its rank will be always even in number. ..
 

Similar threads

Undergrad Un-skewing a skew symmetric matrix (for want of a better phrase)
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Transform a 2x2 matrix into an anti-symmetric matrix
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Reason out the cross product (for the moment): a skew symmetric form
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Unravelling Structure of a Symmetric Matrix
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
4K
High School What Does Skew Symmetry Imply for One-Dimensional Systems?
  • · Replies 3 ·
Replies
3
Views
3K
Graduate What causes a complex symmetric matrix to change from invertible to non-invertible?
  • · Replies 5 ·
Replies
5
Views
3K
Graduate Skew-symmetric matrix property
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Proving the Even Rank of Skew Symmetric Matrices: Induction and Other Methods
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Congruence for Symmetric and non-Symmetric Matrices for Quadratic Form
  • · Replies 7 ·
Replies
7
Views
2K