#### Name

Tishenko Olga Yurievna

#### Scholastic degree

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#### Academic rank

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#### Honorary rank

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#### Organization, job position

Kuban State Agrarian University

#### Web site url

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## Articles count: 1

In 1893, the French mathematician J. Adamar
raised the question: given a matrix of fixed order
with coefficients not exceeding modulo this value,
then what is the maximum modulo value can take
the determinant of this matrix? Adamar fully
decided this question in the case when the
coefficients of the matrix are complex numbers and
put forward the corresponding hypothesis in the
case when the matrix coefficients are real numbers
modulo equal to one. Such matrices satisfying the
Hadamard conjecture were called Hadamard
matrices, their order is four and it is unknown
whether this condition is sufficient for their
existence. The article examines a natural
generalization of the Hadamard matrices over the
field of real numbers, they are there for any order.
This paper proposes an algorithm for the
construction of generalized Hadamard matrices,
and it is illustrated by numerical examples. Also
introduces the concept of constants for the natural
numbers are computed values of this constant for
some natural numbers and shown some
applications of Hadamard constants for estimates
on the top and bottom of the module of the
determinant of this order with arbitrary real
coefficients, and these estimates are in some cases
better than the known estimates of Hadamard. The
results of the article are associated with the results
of the con on the value of determinants of matrices
with real coefficients, not exceeding modulo units