bugGNU Octave - Bugs: bug #52533, Explanation of the rank function

 
 

bug #52533: Explanation of the rank function

Submitted by:  Lasse Kliemann <lassekliemann>
Submitted on:  Mon 27 Nov 2017 05:21:05 PM UTC  
 
Category: DocumentationSeverity: 3 - Normal
Priority: 5 - NormalItem Group: Documentation
Status: FixedAssigned to: Kai Torben Ohlhus <siko1056>
Originator Name: Open/Closed: Closed
Release: devOperating System: Any

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Wed 29 Nov 2017 11:35:57 AM UTC, comment #3:

Pushed: https://hg.savannah.gnu.org/hgweb/octave/rev/f38165f34ff1

Thank you for the documentation improvement.

Kai Torben Ohlhus <siko1056>
Project MemberIn charge of this item.
Wed 29 Nov 2017 10:41:55 AM UTC, comment #2:

Yes, just one little thing:

"The function `orth' may be used to compute an orthonormal basis of that space." --> "The function `orth' may be used to compute an orthonormal basis of the column space." Since although the dimensions are the same, row and column spaces can still be considered as different.

Thanks!

Lasse Kliemann <lassekliemann>
Wed 29 Nov 2017 10:16:42 AM UTC, comment #1:

Do you agree with the following docstring? Then I can push this one straight-forward. The changes will be part of the next major release, that might be 4.4.0, and are contributed to you,
Lasse Kliemann <lasse@lassekliemann.de>.

(file #42520)

Kai Torben Ohlhus <siko1056>
Project MemberIn charge of this item.
Mon 27 Nov 2017 05:21:05 PM UTC, original submission:

https://www.gnu.org/software/octave/doc/interpreter/Basic-Matrix-Functions.html#Basic-Matrix-Functions

Regarding rank, it says: "The rank of a matrix is the number of linearly independent rows or columns and determines how many particular solutions exist to a system of equations. Use null for finding the remaining homogenous solutions."

I find that the statement "how many particular solutions exist to a system of equations" makes no sense. Talking about solutions only makes sense when we have a right-hand side b also given in addition to a coefficient matrix A. It can be said that the system Ax=b is solvable if and only if rank(A) = rank([A b]). If it is solvable, the general solution is given by one particular solution plus the null space. So it makes sense to mention the function 'null' here. However, I do not see why these are the "remaining homogenous solutions".

Here is a suggestion for the text:

"The rank of a matrix is the number of linearly independent rows or columns. It is thus the dimension of the range space. The function 'orth' may be used to compute an orthonormal basis of that space. For testing if a system Ax=b of linear equations is solvable, test if rank(A) = rank([A b]). If it is solvable, a particular solution can be found via A \ b, and the general solution is this particular solution plus the null space, of which a basis can be computed using null(A)."

Lasse Kliemann <lassekliemann>

 

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file #42520:  bug_52533.patch added by siko1056 (2KiB - text/x-patch)

 

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    Follow 6 latest changes.

    Date Changed By Updated Field Previous Value => Replaced By
    Wed 29 Nov 2017 11:35:57 AM UTCsiko1056StatusPatch Submitted=>Fixed
      Open/ClosedOpen=>Closed
    Wed 29 Nov 2017 10:16:42 AM UTCsiko1056Attached File-=>Added bug_52533.patch, #42520
      StatusNone=>Patch Submitted
      Assigned toNone=>siko1056
      Release4.2.1=>dev

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