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Category: Mathematical Definitions

Subject of packing problems

Subject of packing problems

Input interpretation:

Geometry > Computational Geometry > Packing Problems

Topics:

18-point problem | Apollonian gasket | Apollonian network | Barlow packing | bin-packing problem | box-packing theorem | circle covering | circle packing | cookie-cutter problem | cube packing | cubic close packing | de Bruijn’s theorem | disk covering problem | dodecahedral conjecture | ellipsoid packing | five disks problem | Groemer packing | Groemer theorem | Hermite constants | hexagonal close packing | … (total: 53)

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MSC 11A41

MSC 11A41

Input interpretation:

primes (11A41)

Topics:

Brun’s constant | Chebyshev functions | circular prime | Colbert number | even prime | Ferrier’s prime | harmonic series of primes | irregular pair | irregular prime | Mertens constant | Mertens’ second theorem | Mertens theorem | odd prime | permutable prime | prime formulas | prime products | prime representation | prime sums | prime zeta function | primorial | … (total: 33)

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What is a unitary matrix?

What is a unitary matrix?

Input interpretation:

unitary matrix

Definition:

A square matrix U is a unitary matrix if U^H = U^(-1), where U^H denotes the conjugate transpose and U^(-1) is the matrix inverse. For example,

A = [2^(-1/2) | 2^(-1/2) | 0

-2^(-1/2) i | 2^(-1/2) i | 0

0 |  0 | i]

is a unitary matrix. Unitary matrices leave the length of a complex vector unchanged.

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Radon transform

Radon transform

Input interpretation:

Radon transform

Definition:

The Radon transform is an integral transform whose inverse is used to reconstruct images from medical CT scans. A technique for using Radon transforms to reconstruct a map of a planet’s polar regions using a spacecraft in a polar orbit has also been devised. The Radon and inverse Radon transforms will be implemented in a future version of the Wolfram Language as RadonTransform and InverseRadonTransform, respectively.

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