Opened 7 years ago
Closed 7 years ago
#20465 closed enhancement (fixed)
Add "eigendecomposition" to docstring
Reported by:  jmantysalo  Owned by:  

Priority:  trivial  Milestone:  sage7.2 
Component:  documentation  Keywords:  
Cc:  rbeezer, kedlaya  Merged in:  
Authors:  Jori Mäntysalo  Reviewers:  Frédéric Chapoton 
Report Upstream:  N/A  Work issues:  
Branch:  49b57f9 (Commits, GitHub, GitLab)  Commit:  49b57f95a8a273f46bd0520d27b1d89419244c57 
Dependencies:  Stopgaps: 
Description (last modified by )
It took a while to found commands for doing "eigendecomposition", also called "spectral decomposition", to a matrix. Hence I suggest adding those words to documentation of jordan_form()
, so that next one will found them more easy.
Also "Matrix.random(GF(3), 2)
never generates [[2,0],[0,2]]
" must be changed to have Matrix.random(GF(3), 2), algorithm='unimodular')
.
matrix2.pyx
, rref()
has error in link to "echelon_form".
Change History (14)
comment:1 Changed 7 years ago by
Cc:  kedlaya added 

Description:  modified (diff) 
comment:2 Changed 7 years ago by
Description:  modified (diff) 

comment:3 Changed 7 years ago by
Branch:  → u/jmantysalo/add__eigendecomposition__to_docstring 

comment:4 Changed 7 years ago by
Authors:  → Jori Mäntysalo 

Commit:  → b4b58db2c08ad390d390fdd33cd8def2caa712c6 
Status:  new → needs_review 
comment:5 followup: 6 Changed 7 years ago by
I do not believe that the jordon canonical form and the eigen value decomposition are equivalent? I do not know much about this topic, but on this pdf: https://www.mathworks.com/moler/eigs.pdf
Section 10.8(page 16) seems to indicate that the JCF(jordon canonical form) gives a numerically imperfect approximation compared to the Schur form? What am I missing?
comment:6 followup: 7 Changed 7 years ago by
Replying to zonova:
I do not believe that the jordon canonical form and the eigen value decomposition are equivalent? I do not know much about this topic, but on this pdf: https://www.mathworks.com/moler/eigs.pdf
Section 10.8(page 16) seems to indicate that the JCF(jordon canonical form) gives a numerically imperfect approximation compared to the Schur form? What am I missing?
I am not an expert, got this as a comment from a teahcer. Any expert of are here?
Numerical instability is another issue, and does not count if we do not use RR
on other inexact base rign.
The page says "If A
is not defective, then the JCF is the same as the eigenvalue decomposition." So yes, this should be rephrased.
comment:7 followup: 9 Changed 7 years ago by
Replying to jmantysalo:
I am not an expert, got this as a comment from a teahcer. Any expert of are here?
I'm no expert, but afaik the terms “eigendecomposition” and “spectral decomposition” are used for diagonalizable matrices only, while the Jordan form is defined for all matrices (and coincides with the eigendecomposition when the matrix is diagonalizable).
comment:8 Changed 7 years ago by
Commit:  b4b58db2c08ad390d390fdd33cd8def2caa712c6 → 10286f8ce024418658c96634087ad35d44129844 

Branch pushed to git repo; I updated commit sha1. New commits:
10286f8  Eigendecomposition is only defined for diagonalizable matrices.

comment:9 Changed 7 years ago by
Replying to mmezzarobba:
Replying to jmantysalo:
(and coincides with the eigendecomposition when the matrix is diagonalizable).
OK, this corrected.
comment:10 Changed 7 years ago by
Status:  needs_review → needs_work 

sage t long src/sage/matrix/matrix2.pyx Error: TAB character found at lines 9792,9793
comment:11 Changed 7 years ago by
Commit:  10286f8ce024418658c96634087ad35d44129844 → 49b57f95a8a273f46bd0520d27b1d89419244c57 

Branch pushed to git repo; I updated commit sha1. New commits:
49b57f9  Tabs to spaces.

comment:13 Changed 7 years ago by
Reviewers:  → Frédéric Chapoton 

Status:  needs_review → positive_review 
ok, let it be.
comment:14 Changed 7 years ago by
Branch:  u/jmantysalo/add__eigendecomposition__to_docstring → 49b57f95a8a273f46bd0520d27b1d89419244c57 

Resolution:  → fixed 
Status:  positive_review → closed 
New commits:
Trivial additions.