Category:Definitions/Elementary Matrix Operations
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This category contains definitions related to Elementary Matrix Operations.
Related results can be found in Category:Elementary Matrix Operations.
Elementary Row Operation
Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over a field $K$.
The elementary row operations on $\mathbf A$ are operations which act upon the rows of $\mathbf A$ as follows.
For some $i, j \in \closedint 1 m: i \ne j$:
\((\text {ERO} 1)\) | $:$ | \(\ds r_i \to \lambda r_i \) | For some $\lambda \in K_{\ne 0}$, multiply row $i$ by $\lambda$ | ||||||
\((\text {ERO} 2)\) | $:$ | \(\ds r_i \to r_i + \lambda r_j \) | For some $\lambda \in K$, add $\lambda$ times row $j$ to row $i$ | ||||||
\((\text {ERO} 3)\) | $:$ | \(\ds r_i \leftrightarrow r_j \) | Exchange rows $i$ and $j$ |
Elementary Column Operation
Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix over a field $K$.
The elementary column operations on $\mathbf A$ are operations which act upon the columns of $\mathbf A$ as follows.
For some $i, j \in \closedint 1 n: i \ne j$:
\((\text {ECO} 1)\) | $:$ | \(\ds \kappa_i \to \lambda \kappa_i \) | For some $\lambda \in K_{\ne 0}$, multiply column $i$ by $\lambda$ | ||||||
\((\text {ECO} 2)\) | $:$ | \(\ds \kappa_i \to \kappa_i + \lambda \kappa_j \) | For some $\lambda \in K$, add $\lambda$ times column $j$ to column $i$ | ||||||
\((\text {ECO} 3)\) | $:$ | \(\ds \kappa_i \leftrightarrow \kappa_j \) | Interchange columns $i$ and $j$ |
Subcategories
This category has the following 3 subcategories, out of 3 total.
Pages in category "Definitions/Elementary Matrix Operations"
The following 5 pages are in this category, out of 5 total.