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1. Hadamard Property of an Adiabatic KMS State
- wwwitp.physik.tu-berlin.de
- Next: Hadamard states Up: A KMS-like state of Previous: Definition of an adiabatic .
- Hadamard Property of an Adiabatic KMS State.
- In the next section we give a precise definition of a Hadamard state and prove in the following subsection that an adiabatic KMS state is a Hadamard state. ...
- Hadamard states .
- An adiabatic KMS state is a Hadamard state .
- Next: Hadamard states Up: A KMS-like state of Previous: Definition of an adiabatic .
2. Hadamard matrices
- www.maths.gla.ac.uk
- Hadamard matrices.
- Kimura (New Hadamard matrix of order 24, Graphs Combin. 2 (1986) 247-257) who found a Hadamard matrix of order 24 that had been missed by Ito et al (Classification of 3-(24,12,5) designs and 24-dimensional Hadamard matrices, J. ... In my recent paper on Hadamard matrices of orders 24 and 28 that appeared in Discrete Math. ... Had I bothered to check the numbers of Hadamard designs that I had found from the 60 Hadamard matrices of order 24, I would have announced that the correct number of pairwise non-isomorphic 2-(23,11,5) designs is 1106. ...
- Some people may be interested in having the electronic copies of the Hadamard matrices of orders up to 28. ... These can be found in the files Hadamard. 16, Hadamard. 20, Hadamard. 24, Hadamard. ... They are obtained from the normalised Hadamard matrix of order 4m by deleting the first row and column, and replacing the -1's by 0's. ...
- It is a well-known fact that regular two-graphs on 36 vertices correspond to regular symmetric Hadamard matrices with constant diagonal. ... Not all these non-isomorphic regular two-graphs were non-isomorphic as Hadamard matrices. In fact the number of pairwise non-isomorphic Hadamard matrices thus found is 180. These Hadamard matrices were examined for Hadamard designs (symmetric 2-(35,17,8) designs) and I discovered that they yielded 101,863 in number (NOT 108,131 as I wrote in the above paper!!). I include the 180 Hadamard matrices in the file Hadamard. ... This is obtained from the greatest descendant of the Hadamard matrix by concatenating its rows, adding just enough zeros to make the length of the resulting binary integer divisible by 4 and then expressing it as a hexadecimal integer. I also include the order of the automorphism group of the Hadamard matrix as well as the number of non-isomorphic descendants that arise form each. ...
3. M5410 Hadamard Matrices
- math.cudenver.edu
- Hadamard Matrices.
- The applications of Hadamard matrices will be taken up in the following chapters.
- An n x n matrix H = hij is an Hadamard matrix of order n if the entries of H are either +1 or -1 and such that HHt = nI, where Ht is the transpose of H and I is the order n identity matrix. Put another way, a (+1,-1)-matrix is Hadamard if the inner product of two distinct rows is 0 and the inner product of a row with itself is n.
- A few examples check the definition for each of Hadamard matrices are; 1 1 -1 1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 1 1 1 -1 -1 1 1 1 -1 1 -1 -1 1 These matrices were first considered as Hadamard determinants. They were so named because the determinant of an Hadamard matrix satisfies equality in Hadamard's determinant theorem, which states that if X = xij is a matrix of order n where | xij | <= 1 for all i and j, then | det X | <= nn/2.
- It is apparent that if the rows and columns of an Hadamard matrix are permuted, the matrix remains Hadamard. It is also true that if any row or column is multiplied by -1, the Hadamard property is retained. Prove this Thus, it is always possible to arrange to have the first row and first column of an Hadamard matrix contain only +1 entries. An Hadamard matrix in this form is said to be normalized.
- 1 - The order of an Hadamard matrix is 1,2 or 4n, n an integer. ...
- Proof: 1 is an Hadamard matrix of order 1 and the first example above is an Hadamard matrix of order 2. Suppose now that H is an Hadamard matrix of order h > 2. ...
- 2 - If H is a normalized Hadamard matrix of order 4n, then every row (column) except the first has 2n minus ones and 2n plus ones, further n minus ones in any row (column) overlap with n minus ones in each other row (column). ...
- Hadamard matrices are known for many of the possible orders, the smallest order for which the existence of an Hadamard matrix is in doubt is currently 428.
- While there are a great many construction methods for Hadamard matrices, we will only consider one of the simplest, the direct product construction. ...
4. Hermite-Hadamard Inequality
- rgmia.vu.edu.au
- Hermite-Hadamard Type Inequalities .
- Hermite-Hadamard Type Inequalities for Convex Functions .
- Hermite-Hadamard Type Inequalities for Different Kinds of Convexity .
- Hermite-Hadamard Type Inequalities for Convex Functions.
- Keady, A Hadamard-Jensen Inequality and an Application to the Elastic Torsion Problem (dvi).
- Dragomir, On Hadamard's Inequality for the Convex Mappings Defined on a Ball in the Space and Applications (dvi) (pdf).
- Dragomir, On the Hadamard's Inequality for Convex Functions on the Co-ordinates in a Rectangle from the Plane (dvi) (pdf).
- Dragomir, On Hadamard's Inequality for the Convex Mappings Defined on a Disk in the Plane and Connected Results (dvi) (pdf).
- Hermite-Hadamard Type Inequalities for Different Kinds of Convexity.
- Mond, On Hadamard's Inequality for a Class of Functions of Godunova and Levin (dvi) (pdf).
5. Read This: Jacques Hadamard, A Universal Mathematician
- www.maa.org
- Jacques Hadamard, A Universal Mathematician.
- Once called "the living legend of mathematics", Jacques Hadamard (1865-1963) had a tremendous influence on the development of mathematics. As Vladimir Maz'ya and Tatyana Shaposhnikova state in their prologue, despite the "kaleidoscopic conglomeration of methods and ideas" of mathematics in the twentieth century which make an encyclopedic knowledge of it a practical impossibility, "Hadamard was able to know and enhance all areas of mathematics of his time. ...
- In Jacques Hadamard, A Universal Mathematician, Maz'ya and Shaposhnikova create an account of the life of this "living legend" through his own words as well as those of his relatives, friends, and colleagues. Given the profound impact Hadamard has had on mathematics and his various additional interests outside of mathematics, Maz'ya and Shaposhnikova face a daunting objective in writing this book, which they meet quite well through a thorough consideration of his biography and his mathematics.
- This book consists of two major components, one focusing on Hadamard's life and the other describing his various mathematical achievements. Throughout the book, the authors include many relevant photographs, illustrations, letters, and other archival materials, all of which enhance their portrait of Hadamard. In addition, the authors provide many useful sources in their bibliographies, including over 400 references to Hadamard's original works, over 60 references about Hadamard and his legacy, and over 400 other general references. ...
- In the first three hundred or so pages of their book, the authors feature fascinating details of Hadamard's life in late 19th and early 20th century. One illustration of his influence on the mathematical community was le Séminaire Hadamard. As a professor at the Collège de France, Hadamard began in 1913 a seminar which ran for more than 20 years, considered all branches of mathematics, and featured such prominent participants as Borel, Montel, Lebesque, Lévy, Frechet, Weil, Hardy, and many others.
- The authors include firsthand descriptions of Hadamard's close relationships with many leading scholars of his time. ... In his book The Psychology of Invention in the Mathematical Field, Hadamard humbly mentions some of his "failures" in mathematics, such as not discovering the special theory of relativity. As Maz'ya and Shaposhnikova point out, such "admissions of failure are quite rare in mathematical literature, both before and after Hadamard. ...
- Maz'ya and Shaposhnikova offer many glimpses which portray Hadamard not only as a brilliant mathematician, but also as a loving husband and father, an avid collector of ferns, an active participant in politics, and a music enthusiast. For instance, Hadamard was involved in the Dreyfus affair in France at the end of the nineteenth century in which a distant cousin of Hadamard by marriage was found guilty of treason, imprisoned, and then later exonerated as a victim of conspiracy and antisemitism. From that point on, Hadamard was devoted to the fight for human rights and the defense of justice. Another one of Hadamard's interests outside of mathematics was music. This was illustrated during many of Einstein's visits to Paris, when Hadamard would often talk more with him about music than relativity. In fact, Einstein participated as a violinist in an amateur home orchestra created by Hadamard. This text is filled with many such interesting personal tidbits about Hadamard.
6. XviD-devel Hadamard Transform Thoughts
- list.xvid.org
- XviD-devel Hadamard Transform Thoughts .
- Next message: XviD-devel Re: Hadamard Transform Thoughts .
- (at least I guess I did if you get this) I haven't been able to get to that link on the Hadamard transform but have read the discussion in the list archives. I was previously doing a bit of thinking on the H26L Integer Transform and thought maybe some of that would apply to MMXSSE code for Hadamard. The thing I noticed was that the integer transform looked like a Hadamard if the coefficients were all 1 or -1. ... But it seems to me that most of the results of Hadamard could maybe be calculated as the different of 2 averages, each of 4 terms, for instance avg(avg(a,b),avg(c,d)) - avg(avg(e,f),avg(g,h)) where, except for the subtraction, most of it would be done with fast 8x1 byte vectors. ...
- Next message: XviD-devel Re: Hadamard Transform Thoughts .
7. Comb. Structures Lecture Notes on Hadamard Matrices
- www-math.cudenver.edu
- Hadamard Matrices.
- The applications of Hadamard matrices will be taken up in the following chapters.
- An n x n matrix H = hij is an Hadamard matrix of order n if the entries of H are either +1 or -1 and such that HHt = nI, where Ht is the transpose of H and I is the order n identity matrix. Put another way, a (+1,-1)-matrix is Hadamard if the inner product of two distinct rows is 0 and the inner product of a row with itself is n.
- A few examples check the definition for each of Hadamard matrices are; 1 1 -1 1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 1 1 1 -1 -1 1 1 1 -1 1 -1 -1 1 These matrices were first considered as Hadamard determinants. They were so named because the determinant of an Hadamard matrix satisfies equality in Hadamard's determinant theorem, which states that if X = xij is a matrix of order n where | xij | <= 1 for all i and j, then | det X | nn/2.
- It is apparent that if the rows and columns of an Hadamard matrix are permuted, the matrix remains Hadamard. It is also true that if any row or column is multiplied by -1, the Hadamard property is retained. Prove this Thus, it is always possible to arrange to have the first row and first column of an Hadamard matrix contain only +1 entries. An Hadamard matrix in this form is said to be normalized.
- 1 - The order of an Hadamard matrix is 1,2 or 4n, n an integer. ...
- Proof: 1 is an Hadamard matrix of order 1 and the first example above is an Hadamard matrix of order 2. Suppose now that H is an Hadamard matrix of order h > 2. ...
- 2 - If H is a normalized Hadamard matrix of order 4n, then every row (column) except the first has 2n minus ones and 2n plus ones, further n minus ones in any row (column) overlap with n minus ones in each other row (column). ...
- Hadamard matrices are known for many of the possible orders, the smallest order for which the existence of an Hadamard matrix is in doubt is currently 428.
- While there are a great many construction methods for Hadamard matrices, we will only consider one of the simplest, the direct product construction. ...
8. XviD-devel Re: Hadamard Transform Thoughts
- itdp.fh-biergarten.de
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9. BIGpedia - Hadamard matrix - Encyclopedia and Dictionary Online
- www.bigpedia.com
- Hadamard matrix.
- A Hadamard matrix is a square matrix with entries +1, -1 whose rows are mutually orthogonal. From this definition it follows that a Hadamard matrix, H, of order n satisfies .
- A real matrix, M, of order n, with bounded elements, |Mij| ≤1 attains equality in Hadamard's determinant bound .
- if and only if it is a Hadamard matrix. The order of a Hadamard matrix must be 1, 2, or a multiple of 4. The most important open question in the theory of Hadamard matrices is that of existence. The Hadamard conjecture proposes that a Hadamard matrix of order 4k exists for every positive integer k. Following the announcement of the discovery of a Hadamard matrix of order 428 on 21 June 2004 by Hadi Kharaghani and Behruz Tayfeh-Rezaie, the smallest order for which no Hadamard matrix is presently known is 668. ...
- Examples of Hadamard matrices were actually first constructed by James Joseph Sylvester. Let H be a Hadamard matrix of order n. ...
- is a Hadamard matrix of order 2n. Applying this observation repeatedly, starting with the matrix H1, Sylvester constructed Hadamard matrices of order 2k for every non-negative integer k. ...
- Hadamard matrices of orders 12 and 20 were subsequently constructed by Hadamard. Raymond Paley later showed how to construct a Hadamard matrix of order q+1 where q is any power of a prime number which is congruent to 3 modulo 4. ... The Hadamard conjecture should probably be attributed to Paley. Many other methods for constructing Hadamard matrices are now known. ...
10. Genetic Search for Williamson-Type Skew Hadamard Matrices
- www.cs.neu.edu
- Hadamard Matrices.
- Williamson-type Skew Hadamard Matrices (WSHM) have broad application in spectroscopy, communication, and image processing. Hadamard Matrices are composed of ones and minus ones and have the property.
- com/ ~njas/hadamard/index. ... Our approach involves the use of genetic search techniques in which the genetic operators have been modified as a result of the analysis of lower order Hadamard Search Spaces. ...
- We have shown that genetic searches for Williamson-type Skew Hadamard Matrices based on some fitness functions used in exhaustive searches are GA-Hard.
- Lastly we propose a parallel implementation of the genetic search for an arbitrary size Hadamard matrix. ...
11. Quasi-3 Designs and Hadamard Matrices
- www.pims.math.ca
- Quasi-3 Designs and Hadamard Matrices.
- A {\it quasi-3 regular Hadamard matrix} is a square matrix $H$ with entries $\pm 1$, constant row sums, and such that pairs of distinct rows are orthogonal. ... Quasi-3 regular Hadamard matrices are equivalent to certain kinds of quasi-3 symmetric designs. ...
- In this talk I will go over some of the known results on quasi-3 designs and an application in coding theory, describe ongoing attempts to construct new quasi-3 regular Hadamard matrices, and discuss some open problems and the possibility of classifying quasi-3 symmetric designs. ...
12. Une visite au pays des merveilles suggérée par J. Hadamard
- www.univ-tln.fr
- Hadamard.
- Dans cette note, je fais part au lecteur de quelques aspects historiques que j'ai rencontrés au cours de mes lectures sur les matrices de Hadamard : des objets standards de la combinatoire algébrique utilisés dans les télécommunications par la technique dite d'étalement de spectre. ...
- Dans la littérature, les matrices de Hadamard sont des matrices orthogonales dont les coefficients sont tous égaux à +1 ou -1. En d'autres termes, une matrice carrée H de dimension n est une matrice de Hadamard si le produit de H par sa transposée vaut n fois l'identité : .
- La teminologie s'explique par la présence d'un article de Jacques Hadamard (1865-1963), mathématicien bien connu pour ses travaux sur les fonctions analytiques. ...
- Hadamard 8 . ...
- Dans la littérature, les matrices de Hadamard à coefficients complexes sont des matrices de Hadamard généralisées, sont dites réelles, respectivement complexes, celles qui sont à coefficients , respectivement dans l'ensemble des racines quatrièmes de l'unité. Il n'est pas facile de préciser l'ensemble des valeurs de n pour lesquelles il existe une matrice de Hadamard. ...
- on construit la matrice de Hadamard .
- La multiplication d'une colonne ou d'une ligne par un nombre complexe de module 1, l'échange de deux lignes, l'échange de deux colonnes et la transposition engendre un groupe de transformations des matrices carrées qui ne change pas le caractère Hadamard d'une matrice. Deux matrices de Hadamard sont équivalentes si l'une s'obtient à partir de l'autre par une transformation de ce groupe. Sans perdre en généralité, on peut toujours supposer que les trois premières lignes d'une matrice de Hadamard réelle sont : .
- En particulier, mis à part les dimensions 1 et 2, la dimension d'une matrice de Hadamard réelle est un multiple de 4. Aujourd'hui, on sait construire des matrices de Hadamard réelles pour de nombreuses dimensions multiple de 4, voir les ouvrages 2 4 . ...
- Une seconde merveille, attribuée parfois à Jacques Hadamard , mais à tord puisqu elle ne figure pas dans l'article précité. Dans un bref article, Raymond Paley fournit un procédé de construction de matrices de Hadamard, il ajoute : .
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