Vipul: Created page with "{{real square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''Metzler matrix'''', '''quasipositive matrix''', '''quasi-positive..."

2014-05-01T16:28:01Z

Created page with "{{real square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''Metzler matrix'''', '''quasipositive matrix''', '''quasi-positive..."

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{{real square matrix property}}

==Definition==

===Verbal definition===

A [[square matrix]] is termed a '''Metzler matrix'''', '''quasipositive matrix''', '''quasi-positive matrix''', or '''essentially nonnegative matrix''' if all its off-diagonal entries are nonnegative.

===Algebraic description===

Suppose <math>n</math> is a positive integer. A <math>n \times n</math> [[square matrix]] <math>A = (a_{ij})_{1 \le i \le n, 1 \le j \le n}</math> with real entries is termed a '''Metzler matrix'''', '''quasipositive matrix''', '''quasi-positive matrix''', or '''essentially nonnegative matrix''' if it satisfies the following condition:

<math>a_{ij} \ge 0 \ \forall i \ne j \in \{1, 2, \dots, n\}</math>

===Other equivalent descriptions===

A square matrix with real entries is a Metzler matrix if and only if it is the negative of a [[Z-matrix]]. This can be used as an alternative definition.

Metzler matrix - Revision history

Vipul: Created page with "{{real square matrix property}} ==Definition== ===Verbal definition=== A square matrix is termed a '''Metzler matrix'''', '''quasipositive matrix''', '''quasi-positive..."