From: qlli.illb@...
Date: 2014-07-18T01:21:09+00:00
Subject: [ruby-dev:48425] [ruby-trunk - Feature #10056] [Open] [PATCH 0/1]Add #adjugate method to matrix class

Issue #10056 has been reported by gogo tanaka.

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Feature #10056: [PATCH 0/1]Add #adjugate method to matrix class
https://bugs.ruby-lang.org/issues/10056

* Author: gogo tanaka
* Status: Open
* Priority: Normal
* Assignee: 
* Category: 
* Target version: 
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Add Matrix#adjugate to make a matrix adjugate.

Adjugate is really important operator to handle matrix (especially Exploring Data with ruby)

```ruby:
# Property

* Any n-th matrix  `m`(object of Matrix class) Satisfy the following conditions

Matrix.identity(n) == (m.adjugate * m) / m.det

# Differential vector or matrix
Let A = (a(i, j)) is n-th matrix, A(i, j) is adjugate matrix excluding the j and column i row A.

def. ∂det(A)/∂a(i,j) = (-1) ** (i + j) * det(A(i, j))
```

Some people regards adjugate matrix as Hermitian adjoint.

I regard adjuate matrix as transpose of the cofactor matrix by  referencing http://en.wikipedia.org/wiki/Adjugate_matrix.




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