# [R] Null space (or kernel) and image of a matrix

Tue May 31 16:28:40 CEST 2005

```help.search("null space")
gives
Null(MASS)                          Null Spaces of Matrices

http://www.R-project.org/posting-guide.html

David Reiner

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Huntsinger, Reid
Sent: Tuesday, May 31, 2005 9:02 AM
To: 'Aleš Žiberna'; R-help
Subject: RE: [R] Null space (or kernel) and image of a matrix

The null space or kernel of a matrix A would be the subspace of vectors v
such that Av = 0. That is, it's the solution space of a homogeneous linear
system of equations whose coefficients are the rows of A. R implements many
ways to solve such systems. The image is the set of vectors of the form Av
as v ranges over all vectors, which is the same as the span of the columns
of A, aka the column space of A. You can reduce this to a basis or transform
it to an orthogonal basis. Have a look at a linear algebra book to get an
idea for the possibilities.

Reid Huntsinger

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Aleš Žiberna
Sent: Tuesday, May 31, 2005 7:22 AM
To: R-help
Subject: [R] Null space (or kernel) and image of a matrix

Hello!

Does anyone now if there exist a function that would compute a "null space"
(or "kernel" - "Ker") of a matrix and maybe also one that would compute an
"image" ("Im") of a matrix.

I tried R-site search and google, However I found notnihg useful!

Thanks for any sugestions! I am also not sure what an "image" of a matrix
is, so suggestion in this directions  would also be  apreciated.

Aleš Žiberna

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