Category:Examples of Matrix Product
This category contains examples of Matrix Product (Conventional).
Let $\struct {R, +, \circ}$ be a ring.
Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over $R$.
Let $\mathbf B = \sqbrk b_{n p}$ be an $n \times p$ matrix over $R$.
Then the matrix product of $\mathbf A$ and $\mathbf B$ is written $\mathbf A \mathbf B$ and is defined as follows.
Let $\mathbf A \mathbf B = \mathbf C = \sqbrk c_{m p}$.
Then:
- $\ds \forall i \in \closedint 1 m, j \in \closedint 1 p: c_{i j} = \sum_{k \mathop = 1}^n a_{i k} \circ b_{k j}$
Thus $\sqbrk c_{m p}$ is the $m \times p$ matrix where each entry $c_{i j}$ is built by forming the (ring) product of each entry in the $i$'th row of $\mathbf A$ with the corresponding entry in the $j$'th column of $\mathbf B$ and adding up all those products.
This operation is called matrix multiplication, and $\mathbf C$ is the matrix product of $\mathbf A$ with $\mathbf B$.
Pages in category "Examples of Matrix Product"
The following 10 pages are in this category, out of 10 total.
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- Matrix Product (Conventional)/Examples
- Matrix Product (Conventional)/Examples/2 x 2 Real Matrices
- Matrix Product (Conventional)/Examples/3 x 3 Matrix-Vector
- Matrix Product (Conventional)/Examples/Arbitrary 1
- Matrix Product (Conventional)/Examples/Arbitrary 2
- Matrix Product (Conventional)/Examples/Arbitrary 3
- Matrix Product (Conventional)/Examples/Arbitrary 4
- Matrix Product (Conventional)/Examples/Cayley's Motivation
- Matrix Product (Conventional)/Examples/Change of Axes
- Matrix Product (Conventional)/Examples/Column Matrix All 0 except for One 1