Hadamard's theorem (determinants)
GPTKB entity
Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
complex matrices
square matrices real matrices |
| gptkbp:category |
matrix theory
inequalities |
| gptkbp:equalityCondition |
rows are orthogonal and have maximal length
|
| gptkbp:field |
linear algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Hadamard's theorem (determinants)
|
| gptkbp:inequalityType |
determinant bound
|
| gptkbp:namedAfter |
gptkb:Jacques_Hadamard
|
| gptkbp:relatedConcept |
gptkb:Cauchy–Binet_formula
gptkb:Hadamard_matrix matrix norm |
| gptkbp:sentence |
The absolute value of the determinant of a complex matrix with entries of absolute value at most 1 is at most the product of the lengths of the row vectors.
|
| gptkbp:yearProposed |
1893
|
| gptkbp:bfsParent |
gptkb:Jacques_Hadamard
|
| gptkbp:bfsLayer |
6
|