Category:Definitions/Elementary Column Operations

This category contains definitions related to Elementary Column Operations.
Related results can be found in Category:Elementary Column Operations.

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 $j$

Pages in category "Definitions/Elementary Column Operations"

The following 4 pages are in this category, out of 4 total.