What's the difference between a dictionary and a basis?

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SUMMARY

The discussion clarifies the distinction between a "dictionary" and a "basis" in the context of vector spaces and signal processing. A dictionary, as referenced in compressive sensing, serves as a tool for transforming n-dimensional systems into k-dimensional systems, while a basis is a specific set of vectors that spans a vector space. The term "dictionary" is not commonly used outside of signal processing, highlighting its specialized application in this field.

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  • Basic linear algebra, including matrix transformations
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PhillipKP
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I see the term dictionary used a lot and it sounds a lot like a basis for a vector space. But what is the different? Can we collection of vectors be both a basis and a dictionary?

Thanks
 
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Hi PhillipKP! :smile:

Can you give me some kind of reference where the word "dictionary" is used? I have never seen it being used before. :frown:
 
It's used in signal processing and specifically in the new field of compressive sensing.

This is where I first encountered it: http://www-stat.stanford.edu/~candes/papers/CoherentCS.pdf
 
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A dictionary seems to be a tool to translate n-dimensional systems into k-dimensional systems. I don't really see a connection to a basis here. It's just matrix that gives a transformation of signals...

Then again, I know nothing of signal processing...
 
No worries. :)
 

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