Submatrix

Encyclopedia

In mathematics

, a

formed by selecting certain rows and columns from a bigger matrix. That is, as an array, it is cut down to those entries constrained by row

For example

Then

is a submatrix of

The above two methods are common, but there is no standard way to denote a submatrix.

The leters must be difrent in the patern though in determinant

theory is of

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a

**submatrix**is a matrixMatrix (mathematics)

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...

formed by selecting certain rows and columns from a bigger matrix. That is, as an array, it is cut down to those entries constrained by row

*and*column.For example

Then

is a submatrix of

**A**formed by rows 1,2 and columns 1,3,4. This submatrix can also be denoted by**A**(3;2) which means that it is formed by*deleting*row 3 and column 2.The above two methods are common, but there is no standard way to denote a submatrix.

The leters must be difrent in the patern though in determinant

Determinant

In linear algebra, the determinant is a value associated with a square matrix. It can be computed from the entries of the matrix by a specific arithmetic expression, while other ways to determine its value exist as well...

theory is of

*minor determinant*, that is, determinant of a**submatrix.***square*