boolean vector space
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Linear transformations in a Boolean vector space

Mathematische Annalen ◽

10.1007/bf01361188 ◽

1966 ◽

Vol 167 (3) ◽

pp. 240-247 ◽

Cited By ~ 5

Author(s):

P. V. Jagannadham

Keyword(s):

Vector Space ◽

Linear Transformations ◽

Boolean Vector ◽

Boolean Vector Space

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III.—The Eigenvalue Problem for Boolean Matrices

Proceedings of the Royal Society of Edinburgh Section A Mathematical and Physical Sciences ◽

10.1017/s0080454100010712 ◽

1965 ◽

Vol 67 (1) ◽

pp. 25-38

Author(s):

D. E. Rutherford

Keyword(s):

Eigenvalue Problem ◽

Boolean Algebra ◽

Vector Space ◽

Characteristic Equation ◽

Boolean Vector ◽

Boolean Vector Space ◽

The Matrix ◽

Unique Eigenvalue

SynopsisIn the case of Boolean matrices a given eigenvector may have a variety of eigenvalues. These eigenvalues form a sublattice of the basic Boolean algebra and the structure of this sublattice is investigated. Likewise a given eigenvalue has a variety of eigenvectors which form a module of the Boolean vector space. The structure of this module is examined. It is also shown that if a vector has a unique eigenvalue λ, then λ satisfies the characteristic equation of the matrix.