请输入您要查询的字词:

 

单词 Hadamard matrices
释义
Hadamard matrices

Computer
  • A family of matrices, a Hadamard matrix H of order m being an m × m matrix, all of whose elements are either +1 or −1, and such that

    HHT=λI
    where HT is the transpose of H, I is the identity matrix, and λ‎ is a scalar quantity. They are usually written in ‘normalized’ form, i.e. the rows and columns have been signed so that the top row and left column consist of +1 elements only. Hadamard matrices exist only for order m = 1, 2, or 4r for some r. It is known that they exist for all orders m = 2S. It is conjectured, but not known that they exist for all orders m = 4r.

    The rows of any Hadamard matrix form an orthonormal basis, from which property follows many of their applications in the theory of codes, digital signal processing, and statistical sampling. When the order m = 2S, they are called Sylvester matrices.

    A Sylvester matrix has an equivalent matrix whose rows form a set of m-point Walsh functions or, in a different arrangement, Paley functions. Various linear Hadamard codes can be derived from a normalized Sylvester matrix in which +1 has been replaced by 0, and −1 by 1.


随便看

 

科学参考收录了60776条科技类词条,基本涵盖了常见科技类参考文献及英语词汇的翻译,是科学学习和研究的有利工具。

 

Copyright © 2000-2023 Sciref.net All Rights Reserved
京ICP备2021023879号 更新时间:2024/12/25 16:23:15