From: "kernigh (George Koehler)" <xkernigh@...>
Date: 2012-04-14T03:48:22+09:00
Subject: [ruby-core:44344] [ruby-trunk - Bug #6290][Open] Matrix#hermitian? fails to check diagonal elements


Issue #6290 has been reported by kernigh (George Koehler).

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Bug #6290: Matrix#hermitian? fails to check diagonal elements
https://bugs.ruby-lang.org/issues/6290

Author: kernigh (George Koehler)
Status: Open
Priority: Normal
Assignee: 
Category: 
Target version: 
ruby -v: ruby 2.0.0dev (2012-04-14 trunk 35320) [x86_64-openbsd5.0]


=begin
A Hermitian matrix is equal to its own conjugate transpose.

 matrix == matrix.conj.t

The bug is that Matrix#hermitian? fails to check the diagonal elements of the matrix. For example, the matrix in the next script is ((*not*)) Hermitian:

 require 'matrix'
 i = Complex::I
 p Matrix[[-2,   -3-i,   3+i  ],
          [-3+i,  3,    -5-7*i],
          [ 3-i, -5+7*i, 9-4*i]].hermitian?

This script prints (({true})). I expected (({false})), because 9-4*i != 9+4*i. Each diagonal element must equal its own conjugate (so, its imaginary part must be zero).

Matrix#symmetric? can skip the diagonal elements, because each number equals itself. Matrix#hermitian? must not skip the diagonal elements, because some number might not equal its own conjugate.

I attach a git diff with a simple fix to Matrix#hermitian?, and some test.
=end



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