Category:Elementary Column Operations

This category contains results about 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 $j$

Also see

This category has the following 3 subcategories, out of 3 total.

The following 7 pages are in this category, out of 7 total.