Category:Matrix Scalar Product
This category contains results about Matrix Scalar Product.
Let $\GF$ denote one of the standard number systems.
Let $\map \MM {m, n}$ be the $m \times n$ matrix space over $\GF$.
Let $\mathbf A = \sqbrk a_{m n} \in \map \MM {m, n}$.
Let $\lambda \in \GF$ be any element of $\Bbb F$.
The operation of scalar multiplication of $\mathbf A$ by $\lambda$ is defined as follows.
Let $\lambda \mathbf A = \mathbf C$.
Then:
- $\forall i \in \closedint 1 m, j \in \closedint 1 n: c_{i j} = \lambda a_{i j}$
$\lambda \mathbf A$ is the scalar product of $\lambda$ and $\mathbf A$.
Thus $\mathbf C = \sqbrk c_{m n}$ is the $m \times n$ matrix composed of the product of $\lambda$ with the corresponding elements of $\mathbf A$.
Subcategories
This category has the following 2 subcategories, out of 2 total.
Pages in category "Matrix Scalar Product"
The following 4 pages are in this category, out of 4 total.