Category:Negative Matrices

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This category contains results about Negative Matrices.
Definitions specific to this category can be found in Definitions/Negative Matrices.

Let $\GF$ denote one of the standard number systems.

Let $\map \MM {m, n}$ be a $m \times n$ matrix space over $\GF$.

Let $\mathbf A = \sqbrk a_{m n}$ be an element of $\map \MM {m, n}$.

Then the negative (matrix) of $\mathbf A$ is denoted and defined as:

$-\mathbf A := \sqbrk {-a}_{m n}$
\(\ds -\mathbf A\) \(=\) \(\ds -1 \mathbf A\)
\(\ds \) \(=\) \(\ds \sqbrk {-a}_{m n}\)


$-1 \mathbf A$ denotes the matrix scalar product of $-1$ with $\mathbf A$
$-a$ is the negative of $a$.