characterization of tight frames in n

Question 1.

What conditions must the vectors {xi}i=1kRn satisfy in order to be a tight frame in Rn?


Let E be the k×n matrix whose rows are the vectors {xi}i=1k:


Then the tight frame condition i=1k|x,xi|2=Ax2 gives (Ex)TEx=AxTx for all xn, or ETE=AIn:


Therefore, the vectors


are an A-tight frame iff the vectors


i.e., the columns of E, are all of norm A and form an orthogonalMathworldPlanetmathPlanetmath family.

Title characterizationMathworldPlanetmath of tight frames in n
Canonical name CharacterizationOfTightFramesInmathbbRn
Date of creation 2013-03-22 14:27:08
Last modified on 2013-03-22 14:27:08
Owner swiftset (1337)
Last modified by swiftset (1337)
Numerical id 5
Author swiftset (1337)
Entry type Result
Classification msc 46C99