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[Octave-bug-tracker] [bug #52533] Explanation of the rank function
From: |
Lasse Kliemann |
Subject: |
[Octave-bug-tracker] [bug #52533] Explanation of the rank function |
Date: |
Mon, 27 Nov 2017 12:21:06 -0500 (EST) |
User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:52.0) Gecko/20100101 Firefox/52.0 |
URL:
<http://savannah.gnu.org/bugs/?52533>
Summary: Explanation of the rank function
Project: GNU Octave
Submitted by: lassekliemann
Submitted on: Mon 27 Nov 2017 05:21:05 PM UTC
Category: Documentation
Severity: 3 - Normal
Priority: 5 - Normal
Item Group: Documentation
Status: None
Assigned to: None
Originator Name:
Originator Email:
Open/Closed: Open
Discussion Lock: Any
Release: 4.2.1
Operating System: Any
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Details:
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)."
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- [Octave-bug-tracker] [bug #52533] Explanation of the rank function,
Lasse Kliemann <=