Frame of a vector space

In linear algebra, a frame of an inner product space is a generalization of a basis of a vector space to sets that may be linearly dependent. In the terminology of signal processing, a frame provides a redundant, stable way of representing a signal. Frames are used in error detection and correction and the design and analysis of filter banks and more generally in applied mathematics, computer science, and engineering.

Suppose we have a set of vectors ${\displaystyle \{\mathbf {e} _{k}\}}$ in the vector space V and we want to express an arbitrary element ${\displaystyle \mathbf {v} \in V}$ as a linear combination of the vectors ${\displaystyle \{\mathbf {e} _{k}\}}$, that is, we want to find coefficients ${\displaystyle c_{k}}$ such that

...
Wikipedia