Hello.
I'm trying to grasp the notation for the definition of something called the weak q-norm, defined as
\|x\|_{q,w}^q = \sup\limits_{\epsilon > 0} \epsilon^q \left| \Big\{i \,|\, |x_i| > \epsilon \Big\} \right|
I don't come from a pure math background so I've never seen this...
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
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
There is a relationship between the index, optical path length, and phase. The higher the index, the more the optical path length, and the more the phase delay a light will have as it traverses a piece of glass.
The point of a converging (aka positive aka convex) lens is to induce more...
Homework Statement
Theorem: Prove that \mathbb{F}^{\infty} infinite dimensionalHomework Equations
Definition of Infinite Dimensional Vector Space: A vector space that
is not finite dimension
Definition of Finite Dimensional Vector Space: \exists list of vectors
in it that spans the space...
Homework Statement
Hi I'm trying to prove that the sum of two subspaces U and W is also a subspace.
Homework Equations
U is a subspace of V if U is also a vector space and it contains the additive identity, is closed under addition, and closed under scalar multiplication.
The definition of...