The Hamel type and Schauder type of this mathematical obejct differ in the cardinality of allowed combinations.  SVD algorithms relate one of these to a diagonal matrix, while the spectral theorem allows the decomposition into one of these constructed from eigenvectors.  The Fourier transform is equivalent to changing betwe
The Hamel type and Schauder type of this mathematical obejct differ in the cardinality of allowed combinations.  SVD algorithms relate one of these to a diagonal matrix, while the spectral theorem allows the decomposition into one of these constructed from eigenvectors.  The Fourier transform is equivalent to changing between the (*) position type and the momentum type of these objects.  Zorn's lemma can show every vector space is entitled to one of these, and any linearly independent set can be extended into one.  For 10 points, name this class of mathematical objects, a linearly independent set of vectors spanning some space.
The Hamel type and Schauder type of this mathematical obejct differ in the cardinality of allowed combinations.  
{basis}