# Category:Elementary Column Operations

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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

## Subcategories

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

## Pages in category "Elementary Column Operations"

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

### E

- Effect of Elementary Column Operations on Determinant
- Elementary Column Matrix for Inverse of Elementary Column Operation is Inverse
- Elementary Column Operations as Matrix Multiplications
- Elementary Column Operations as Matrix Multiplications/Corollary
- Elementary Matrix corresponding to Elementary Column Operation
- Exchange of Columns as Sequence of Other Elementary Column Operations
- Existence of Inverse Elementary Column Operation