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Spark vs Rank of a matrix


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I understand the rank of a matrix to be the maximum number of linearly independent rows (or equivalently columns) in a matrix. 

The spark seems to be the minimum number of columns which are linearly dependent. 

I'm missing some subtlety because these seem to me to be the same thing. Does anyone know any good resources on the distinction, i could only find the wikipedia page and that is a bit sparse

 

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  • 1 year later...

The statement "the spark of a matrix is zero" expands to mean "There is a set of columns of size zero that is linearly dependent." Which isn't true.

Spark of a full rank matrix is something of a convention. Spark increases as linear dependence decreases - and a full rank matrix is maximally linearly independent, so you want the spark to be large, not small. Choosing it to be infinity is likely the best convention. 

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