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Mutual Coherence (other)
Mutual coherence can refer to: * Mutual coherence (physics), sinusoidal waves which exhibit a constant phase relationship * Mutual coherence (linear algebra) In linear algebra, the coherence or mutual coherence of a matrix ''A'' is defined as the maximum absolute value of the cross-correlations between the columns of ''A''. Formally, let a_1, \ldots, a_m\in ^d be the columns of the matrix ''A'', whic ..., a property of a matrix describing the maximum correlation between its columns See also * Coherence (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Coherence (physics)
In physics, two wave sources are coherent if their frequency and waveform are identical. Coherence is an ideal property of waves that enables stationary (i.e., temporally or spatially constant) interference. It contains several distinct concepts, which are limiting cases that never quite occur in reality but allow an understanding of the physics of waves, and has become a very important concept in quantum physics. More generally, coherence describes all properties of the correlation between physical quantities of a single wave, or between several waves or wave packets. Interference is the addition, in the mathematical sense, of wave functions. A single wave can interfere with itself, but this is still an addition of two waves (see Young's slits experiment). Constructive or destructive interference are limit cases, and two waves always interfere, even if the result of the addition is complicated or not remarkable. When interfering, two waves can add together to create a wave of g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mutual Coherence (linear Algebra)
In linear algebra, the coherence or mutual coherence of a matrix ''A'' is defined as the maximum absolute value of the cross-correlations between the columns of ''A''. Formally, let a_1, \ldots, a_m\in ^d be the columns of the matrix ''A'', which are assumed to be normalized such that a_i^H a_i = 1. The mutual coherence of ''A'' is then defined as :M = \max_ \left, a_i^H a_j \. A lower bound is : M\ge \sqrt A deterministic matrix with the mutual coherence almost meeting the lower bound can be constructed by Weil's theorem. This concept was reintroduced by David Donoho and Michael Elad in the context of sparse representations. A special case of this definition for the two-ortho case appeared earlier in the paper by Donoho and Huo. The mutual coherence has since been used extensively in the field of sparse representations of signals. In particular, it is used as a measure of the ability of suboptimal algorithms such as matching pursuit and basis pursuit to correctly identif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
