Talk:Kernel (matrix)

message: Can somebody make a multi-dimesional example here? (more than one free variable....)
I am for the idea of merging this article (Null Space), with Kernel
-- minghan 15:23, 26 January 2006 (UTC)
replies: text: I would prefer to have kernel (mathematics) continue to focus on the more general case while this article addresses the restricted case of kernels of matrix operators in linear algebra. Deco 02:33, 27 January 2006 (UTC)
replies: text: Changed my mind. This article presents itself as the same concept as kernels, so a merge is warranted. Deco 02:35, 27 January 2006 (UTC)

text: A slight philosophical difference is that a matrix is not a map, whereas a linear transformation is, even though the two are commonly identified.  The null space of a matrix refers to what would be the kernel if we thought of it as a linear transformation.  Whether the articles are written this way, I don't know, but I think that at least in theory, the two should be considered separate concepts, that you realize are the same after a little bit of thinking.
Hmmm.  I still suggest that the merge discussion be centralized in kernel (mathematics). — Arthur Rubin | (talk) 02:57, 17 March 2006 (UTC)
thread_title:  untitled 

message: "Nullity" should no longer redirect here, since it appears that someone has managed to solve the "divide by zero problem"... and the solution is called Nullity. (http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml) Medevilenemy 19:24, 6 December 2006 (UTC)
replies: text: No offense, but that "solution" is total bullcrap. --Wooty Woot? contribs 09:54, 7 December 2006 (UTC)
replies: text: It's not Wikipedia's job to decide whether a theory is correct or not. Leave that to discussion within the mathematics community and related journals. See the note at the bottom of WP:NOR. --Tjohns   ✎ 12:03, 7 December 2006 (UTC)

text: I think discussion regarding this should take place over at Talk:Nullity. --Tjohns   ✎ 12:00, 7 December 2006 (UTC)
thread_title: Division by Zero

message: I am sure this is very obvious to most of you but I was curious to see at the end of the article a method for computing the null space using QR factorization. I am not a mathematician myself but was wondering what is the proof that A Q2 = 0? It may be staring me in the face but I don't see it at the moment, I am sure it is correct as I tried the method using SciLab and it worked very nicely. --Rhoddydog (talk) 17:35, 14 August 2008 (UTC)
thread_title:  Proof that A Q2 = 0 

message: Can I remove the paragraph from this page and put it on a separate "left nullspace" page? It's nice when you search for something if you just get the information you want instead of a whole bunch of other stuff.daviddoria (talk) 15:46, 19 September 2008 (UTC)
thread_title: Split Left Nullspace

message: Hi there,
I thought it would be nice if there would be a section explaining the relation between the nullspace and the eigenvalues/eigenvectors of the matrix.
As far as I know, the dimension of the nullspace (nullity?) of a matrix is equal to the amount of eigenvectors with eigenvalue 0. And the nullspace is spanned by these vectors, too. 
Drugbird (talk) 07:56, 27 April 2010 (UTC)
thread_title:  Relation to eigenvalues 

message: The current algorithm given using RRE to find a nullspace has a step "Interpreting the reduced row echelon form as a homogeneous linear system" and then "determine which of the variables are free".  That's a bit of a stretch for someone who is just learning how to calculate nullspace.  I'd suggest a more concrete algorithm for it, like the following:
# If the input matrix is wider than it is tall, pad zero rows to make it square.
# Put the matrix in RRE form keeping the pivots along the diagonal.
# If the matrix is taller than it is wide, crop the lower rows to make it square (they will all be zero rows if the RRE was done correctly).
# Subtract the identity matrix.
That produces a null space basis from the non zero columns of the result.  It is simple, uses RRE, and doesn't require the "now write out tons of expressions and modify them" step. Antares5245 (talk) 06:37, 28 August 2010 (UTC)
thread_title:  Using RRE to calculate Nullspace 

message: It seems that using the LQ factorization would be faster at finding the null space than the QR factorization, since we can apply it directly to the matrix $A$ instead of to $A^T$. LAPACK has routines for computing the LQ factorization as well.Vinzklorthos (talk) 15:13, 6 February 2012 (UTC)
thread_title:  LQ Factorization 

message: I have completely rewritten, and renamed this section into "Computation of the null space in a computer". In fact, the previous version did not respect WP:NPOV by supposing that every numerical computation is a floating-point computation, which is a blatant mistake. On the other hand I have removed the large part of the section devoted to specific numerical algorithms, because it is outside the scope of this article. In fact, null space computation is a special instance of solving a homogeneous linear system. Deciding which algorithm is the best in each case is a highly technical matter, whose answer depend on various parameters of the input matrix (its structure) as well as the architecture (cache(s), vectorization, number of cores, size of the memory, ...) of the computer. Implementing a high performance linear algebra package is yet a research project for a whole team! Thus the questions, that were addressed in the part that I have removed, have not their place here but in an article high performance liner algebra, yet to write. Also the suppressed part presented a single algorithm as the state of the art. This is WP:OR --D.Lazard (talk) 16:42, 19 October 2012 (UTC)
thread_title:  Numerical computation of null space  

message: Substituted at 02:16, 5 May 2016 (UTC)
thread_title: Assessment comment