Opened 7 years ago

Closed 7 years ago

#20465 closed enhancement (fixed)

Add "eigendecomposition" to docstring

Reported by: jmantysalo Owned by:
Priority: trivial Milestone: sage-7.2
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:

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Description (last modified by jmantysalo)

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 jmantysalo

Cc: ​kedlaya added
Description: modified (diff)

comment:2 Changed 7 years ago by jmantysalo

Description: modified (diff)

comment:3 Changed 7 years ago by jmantysalo

Branch: u/jmantysalo/add__eigendecomposition__to_docstring

comment:4 Changed 7 years ago by jmantysalo

Authors: Jori Mäntysalo
Commit: b4b58db2c08ad390d390fdd33cd8def2caa712c6
Status: newneeds_review

New commits:

b4b58dbTrivial additions.

comment:5 Changed 7 years ago by 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?

comment:6 in reply to:  5 ; Changed 7 years ago by jmantysalo

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 in reply to:  6 ; Changed 7 years ago by mmezzarobba

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 git

Commit: b4b58db2c08ad390d390fdd33cd8def2caa712c610286f8ce024418658c96634087ad35d44129844

Branch pushed to git repo; I updated commit sha1. New commits:

10286f8Eigendecomposition is only defined for diagonalizable matrices.

comment:9 in reply to:  7 Changed 7 years ago by jmantysalo

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 chapoton

Status: needs_reviewneeds_work
sage -t --long src/sage/matrix/matrix2.pyx
    Error: TAB character found at lines 9792,9793

comment:11 Changed 7 years ago by git

Commit: 10286f8ce024418658c96634087ad35d4412984449b57f95a8a273f46bd0520d27b1d89419244c57

Branch pushed to git repo; I updated commit sha1. New commits:

49b57f9Tabs to spaces.

comment:12 Changed 7 years ago by jmantysalo

Status: needs_workneeds_review

Arghs. Emacs and .py vs. .pyx.

comment:13 Changed 7 years ago by chapoton

Reviewers: Frédéric Chapoton
Status: needs_reviewpositive_review

ok, let it be.

comment:14 Changed 7 years ago by vbraun

Branch: u/jmantysalo/add__eigendecomposition__to_docstring49b57f95a8a273f46bd0520d27b1d89419244c57
Resolution: fixed
Status: positive_reviewclosed
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