A Metric Space for Series of Spectra of Type Ia Supernovae

A metric space for the study of large samples of spectral series of type Ia supernovae is introduced. The method is built to be intrinsically independent from dust extinction and estimates of the distance and its validity is confirmed by checking a number of known relations. The resulting metric space is ideal for a number of applications. Some are investigated in detail: assess spectral series of models, calibrate near infrared luminosity, and study the extinction-reddening relation.