Physical Sciences and Mathematics Commons^™

Constructions Of Hadamard Matrices, Jacob Steepleton

Chancellor’s Honors Program Projects

No abstract provided.

Classification Results Of Hadamard Matrices, Gregory Allen Schmidt

Masters Theses

In 1893 Hadamard proved that for any n x n matrix A over the complex numbers, with all of its entries of absolute value less than or equal to 1, it necessarily follows that

|det(A)| ≤ n^n/2 [n raised to the power n divided by two],

with equality if and only if the rows of A are mutually orthogonal and the absolute value of each entry is equal to 1 (See [2], [3]). Such matrices are now appropriately identified as Hadamard matrices, which provides an active area of research in both theoretical and applied fields …

Constant Rank Matrices, Harlan D. Mills

The Harlan D. Mills Collection

A matrix is a rectangular array of quantities which, as an array, obeys certain rules when combined with other matrices by the operations of addition and multiplication, or when combined with scalar quantities by the operation of multiplication. These operations have meaning if and only if the matric quantities and scalar quantities are elements of a ring. A minor of a matrix is a certain function of a square sub-array of the matrix, and has a unique meaning if and only if the elements of the sub-array are commutative. The rank of a matrix is a function of all possible …