▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Binary cartesian set product
▾ Binary relation
▾ Map
▾ Countable map
▾ Array
▾ Matrix
▾ Toeplitz matrix
Diagonal matrix
Formulation 0
Let $R$ be a D24: Ring such that
(i) $0_R$ is an D270: Additive identity in $R$
A D102: Matrix $r : I \times J \to R$ is a diagonal matrix over $R$ if and only if \begin{equation} \forall \, i \in I : \forall \, j \in J \left( i \neq j \quad \implies \quad r_{i, j} = 0_R \right) \end{equation}
Child definitions
» D5858: Diagonal complex matrix
» D761: Identity matrix