Opened 10 years ago

Closed 10 years ago

# Linear dependence/independence of vectors

Reported by: Owned by: rbeezer jason, was minor sage-4.7.2 linear algebra sage-4.7.2.alpha2 Rob Beezer Ivo Hedtke N/A #10746

This routine is really intended for instructional use. It makes it clear that linear independence is a property of a set of vectors from a vector space, thus its placement in the module code. It is much quicker for the experienced user to just ask for a kernel, but I intend to make this available to students for discussions of vector spaces in their own right, before discussing subspaces such as the kernel of a matrix. As a bonus, an empty set as a return value is equivalent to linear independence.

Depends:

1. #10746

Apply:

1. trac_11535-linear-dependence-vectors.patch

### comment:1 Changed 10 years ago by rbeezer

• Authors set to Rob Beezer
• Dependencies set to #10746
• Description modified (diff)
• Status changed from new to needs_review

Patch depends #10746, which is merged in 4.7.1.alpha2.

### comment:2 follow-up: ↓ 3 Changed 10 years ago by hedtke

• Reviewers set to Ivo Hedtke
• Status changed from needs_review to positive_review
• OK: works
• OK doctest coverage: SCORE /sage/modules/free_module.py: 96% (165 of 171) documentation for the new function is NOT missing
• OK: long doctests
• OK docbuild reference html
• OK documentation of the new function is good, with many examples

### comment:3 in reply to: ↑ 2 Changed 10 years ago by rbeezer

• Description modified (diff)

Ivo,

Many thanks for the review - this is being used a lot already in my linear algebra textbook, so it's great to get it in now.

Rob

### comment:4 Changed 10 years ago by jdemeyer

• Milestone changed from sage-4.7.1 to sage-4.7.2

### comment:5 Changed 10 years ago by jdemeyer

• Merged in set to sage-4.7.2.alpha2
• Resolution set to fixed
• Status changed from positive_review to closed
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