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Overcompleteness
Overcompleteness is a concept from linear algebra that is widely used in mathematics, computer science, engineering, and statistics (usually in the form of overcomplete frames). It was introduced by R. J. Duffin and A. C. Schaeffer in 1952. Formally, a subset of the vectors \_ of a Banach space In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ... X, sometimes called a "system", is complete if every element in X can be approximated arbitrarily well Norm (mathematics)#Equivalence, in norm by finite linear combinations of elements in \_.C. Heil, A Basis Theory Primer: Expanded Edition. Boston, MA: Birkhauser, 2010. A complete system is additionally overcomplete if there exists a \phi_j which can be removed from the system while maintaining completeness (i.e., \exists j : \_ \text). In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Gabor
Dennis Gabor ( ; hu, Gábor Dénes, ; 5 June 1900 – 9 February 1979) was a Hungarian-British electrical engineer and physicist, most notable for inventing holography, for which he later received the 1971 Nobel Prize in Physics. He obtained British citizenship in 1934, and spent most of his life in England. Life and career Gabor was born as Günszberg Dénes, into a Jewish family in Budapest, Hungary. In 1918, his family converted to Lutheranism. Dennis was the first-born son of Günszberg Bernát and Jakobovits Adél. Despite having a religious background, religion played a minor role in his later life and he considered himself agnostic. In 1902, the family received permission to change their surname from Günszberg to Gábor. He served with the Hungarian artillery in northern Italy during World War I. He began his studies in engineering at the Technical University of Budapest in 1918, later in Germany, at the Charlottenburg Technical University in Berlin, now known as t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
