Linear Algebra

Echelon form (Row echelon form, ref)

A rectangular matrix is in echelon form if it has the following properties.

1. All nonzero rows are above any rows of all zeros.

2. Each leading entry of a row is in a column to the right of the leading entry of the row above it.

3. All entries in a column below a leading entry are zeros.

Reduced echelon form (Row reduced echelon form, rref)

1. All nonzero rows are above any rows of all zeros.

2. Each leading entry of a row is in a column to the right of the leading entry of the row above it.

3. All entries in a column below a leading entry are zeros.

4. The leading entry in each nonzero row is 1.

5. Each leading 1 is the only nonzero entry in its column.

Identity Matrix

(Must be a square matrix)

Domain and Codomain

In a transformation (or function or mapping) T from Rⁿ to R^m, The set Rⁿ is called the domain of T, and R^m is the called the codomain of T.