Category:Definitions/Echelon Matrices
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This category contains definitions related to Echelon Matrices.
Related results can be found in Category:Echelon Matrices.
Let $\mathbf A = \sqbrk a_{m n}$ be an $m \times n$ matrix.
Echelon Form
$\mathbf A$ is in echelon form if and only if:
- $(1): \quad$ The leading coefficient in each non-zero row is $1$
- $(2): \quad$ The leading $1$ in any non-zero row occurs to the right of the leading $1$ in any previous row
- $(3): \quad$ The non-zero rows appear before any zero rows.
Reduced Echelon Form
The matrix $\mathbf A$ is in reduced echelon form if and only if, in addition to being in echelon form, the leading $1$ in any non-zero row is the only non-zero element in the column in which that $1$ occurs.
Such a matrix is called a reduced echelon matrix.
Subcategories
This category has only the following subcategory.
G
Pages in category "Definitions/Echelon Matrices"
The following 17 pages are in this category, out of 17 total.
E
- Definition:Echelon Form
- Definition:Echelon Matrix
- Definition:Echelon Matrix/Also defined as
- Definition:Echelon Matrix/Also known as
- Definition:Echelon Matrix/Echelon Form
- Definition:Echelon Matrix/Echelon Form/Non-Unity Variant
- Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Also defined as
- Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 1
- Definition:Echelon Matrix/Echelon Form/Non-Unity Variant/Definition 2
- Definition:Echelon Matrix/Reduced Echelon Form