Hallo zusammen,

DimEigenraum: (n-rank(A-λ*E))=1@#
should be 2
some steps of elementary row additions later
is 2

https://de.smath.com/cloud/sheet/vooDFR4FbP

any idea whats wrong?

Wrote

https://de.smath.com/cloud/sheet/vooDFR4FbP

This link doesn't works, be sure to use the share button link (on the right of the save button), because the address bar link is restricted to the author only.

Upps, sorry

Made a link
https://de.smath.com/cloud/worksheet/3BgYDE7e,


Maxima pure
(%i6) A: matrix([1,1,1,-1,0],[0,1,0,0,1],[0,0,0,1,0],[0,0,-1,2,1],[0,0,0,0,1])$
(%i7) A-1*ident(5)$
(%i5) rank(A-1*ident(5));
(%o5) 3
but
Maxima(rank(A-1*identity(5)))=4
or
DimEigenraum: (n-rank(A-λ*E))=1

The referenced sheet seems to use Maxima(). This doesn't work, as third party plug-ins aren't available in the cloud version.
It is better to attach such files here.

rank(M) ... matrix rank is Smath built-in.
Here is a most precious application.

Matrix PseudoInverse.sm (111,21 KiB) scaricato 1232 volta(e).

Wrote

rank(M) ... matrix rank is Smath built-in.
Matrix PseudoInverse.sm (111,21 KiB) scaricato 1232 volta(e).

and in how far do your example explain the incorrect calculation

Wrote

The referenced sheet seems to use Maxima(). This doesn't work, as third party plug-ins aren't available in the cloud version.
It is better to attach such files here.

the Maxima part calculate the single eigenvalue which is set manually in cloud version



JordanMatrix5x5-5fachEW-HV.1.2.Stufe .sm (47,19 KiB) scaricato 1190 volta(e).

Hi. You're right, it's a bug and there are no way to make this works (numerical nor symbolic):



First column is zero and 3th = - 4th columns, so can't be rank = 4.

Best regards.

Alvaro.

Wrote

and in how far do your example explain the incorrect calculation

Just advanced maths above the classroom.
Your example replies bug from incorrectly threaded input.
As given, your [5*5] matrix has no mathematical meaning.

Page1 rank.sm (11,74 KiB) scaricato 1361 volta(e).

... clean the bugger
What application do you have for "rank(,) ?
Don't confuse with Rank in Data Analysis.
rref [Row Reduce Echelon Function] is a damned long monkey business.
Has it been done in Smath ... Watson ?

... Rank(V)
Given a set of data values, the rank of each value is the position
at which that value appears in a sorted list of the data.
When values repeat, the rank is an average of the indices where
the value occurs after sorting.