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: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Aleš 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. Aleš Žiberna ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
