Scrabble?! OVERCOMPLEX

Definitions of OVERCOMPLEX in various dictionaries:

In linear algebra, a subset of the vectors { ϕ i } i ∈ J {\displaystyle \{\phi _{i}\}_{i\in J}} of a Banach space X {\displaystyle X} , sometimes called a "system", is complete if every element in X {\displaystyle X} can be approximated arbitrarily well in norm by finite linear combinations of elements in { ϕ i } i ∈ J {\displaystyle \{\phi _{i}\}_{i\in J}} . Such a complete system is overcomplete if removal of a ϕ j {\displaystyle \phi _{j}} from the system results in a system (i.e., { ϕ i } i ∈ J ∖ { j } {\displaystyle \{\phi _{i}\}_{i\in J\backslash \{j\}}} ) that is still complete. In different research, such as signal processing and function approximation, overcompleteness can help researchers to achieve a more stable, more robust, or more compact decomposition than using a basis. Overcomplete frames are widely used in mathematics, computer science, engineering, and statistics.