Category:Examples of Matrix Entrywise Addition
This category contains examples of Matrix Entrywise Addition.
Let $\mathbf A$ and $\mathbf B$ be matrices of numbers.
Let the orders of $\mathbf A$ and $\mathbf B$ both be $m \times n$.
Then the matrix entrywise sum of $\mathbf A$ and $\mathbf B$ is written $\mathbf A + \mathbf B$, and is defined as follows:
Let $\mathbf A + \mathbf B = \mathbf C = \sqbrk c_{m n}$.
Then:
- $\forall i \in \closedint 1 m, j \in \closedint 1 n: c_{i j} = a_{i j} + b_{i j}$
Thus $\mathbf C = \sqbrk c_{m n}$ is the $m \times n$ matrix whose entries are made by performing the adding corresponding entries of $\mathbf A$ and $\mathbf B$.
That is, the matrix entrywise sum of $\mathbf A$ and $\mathbf B$ is the Hadamard product of $\mathbf A$ and $\mathbf B$ with respect to addition of numbers.
This operation is called matrix entrywise addition.
Pages in category "Examples of Matrix Entrywise Addition"
The following 6 pages are in this category, out of 6 total.
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- Matrix Entrywise Addition forms Abelian Group/Examples
- Matrix Entrywise Addition forms Abelian Group/Examples/2x2 Matrices over Rational Numbers
- Matrix Entrywise Addition forms Abelian Group/Examples/nxn Matrices over Real Numbers
- Matrix Entrywise Addition/Examples
- Matrix Entrywise Addition/Examples/Arbitrary Matrices 1
- Matrix Entrywise Addition/Examples/Real 2 x 2