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Hadamard Matrices and Their Applications

Posted By: step778
Hadamard Matrices and Their Applications

S.S. Agaian, "Hadamard Matrices and Their Applications"
1985 | pages: 230 | ISBN: 3540160566 | PDF | 7 mb

The importance of orthouonal matrices in modern discrete mathematics and its applications is well known; for many applied problems (for example, for construction of discrete equipments realizing fast or orthogonal transformations) one needs consideration of integer orthogonal matrices and in particular, orthogonal matrices with the elements -I and +I. Square orthogonal matrices with the elements -Iand +I are called Hadamard matrices.
Investigations of Hadamard matrices were connected initially with a linear algebra problems (for example, with finding maximum of determinant). Later on it turned out that the applications of Hadamard matrices in questions connected with information transfer by non-line electromagnetic waves, with automaton training and with a number of question from information theory (information compression and noiseless coding, optimal linear detection of a signal through noise, construction of multiple-access chanels) are also fruitful. Besides it turned out that there are interrelations between Hadamard matrices and different combinatorial configurations such as block-designs, Latin square orthogonal F-square configurations, correcting codes, finite geometties, strongly regular graphs. These interrelations allow to investigate the properties of different objects using the analogy in their structures.

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