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 Various linear Hadamard codes can be derived from a normalized Sylvester matrix in which +1 has been replaced by 0, and –1 by 1.
"Hadamard matrices." A Dictionary of Computing. . Encyclopedia.com. (August 19, 2018). http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/hadamard-matrices
"Hadamard matrices." A Dictionary of Computing. . Retrieved August 19, 2018 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionaries-thesauruses-pictures-and-press-releases/hadamard-matrices
Encyclopedia.com gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).
Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.
Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, Encyclopedia.com cannot guarantee each citation it generates. Therefore, it’s best to use Encyclopedia.com citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:
Modern Language Association
The Chicago Manual of Style
American Psychological Association
- Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most Encyclopedia.com content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
- In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.