In mathematics, a **submatrix** is a matrix 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 corresponding concept in determinant theory is of *minor determinant*, that is, determinant of a * square* submatrix.

### Other articles related to "submatrix":

Communication Complexity - Formal Definition

... eliminates a set of rows/columns resulting in a

... eliminates a set of rows/columns resulting in a

**submatrix**of A ... Equivalently, R can also be viewed as a**submatrix**of the input matrix A such that R = M N where M X and N Y ... is } Then, X Y, and is a rectangle and a**submatrix**of A ...Matrix (mathematics) - Basic Operations -

... A

**Submatrix**... A

**submatrix**of a matrix is obtained by deleting any collection of rows and/or columns. 3-by-4 matrix, we can construct a 2-by-3**submatrix**by removing row 3 and column 2 The minors and cofactors of a matrix are found by computing the ...Nullity Theorem

... Nguyen 2004) More generally, if a

... Nguyen 2004) More generally, if a

**submatrix**is formed from the rows with indices {i1, i2, …, im} and the columns with indices {j1, j2, …, jn}, then the complementary**submatrix**is formed from the rows with ... The nullity theorem states that the nullity of any**submatrix**equals the nullity of the complementary**submatrix**of the inverse ...Dantzig–Wolfe Decomposition - Required Form

... into independent submatrices such that if a variable has a non-zero coefficient within one

... into independent submatrices such that if a variable has a non-zero coefficient within one

**submatrix**, it will not have a non-zero coefficient in another**submatrix**... Note that it is possible to run the algorithm when there is only one F**submatrix**...Greatest Common Divisor Of Two Polynomials - Univariate Polynomials With Coefficients in A Field - Subresultants - Technical Definition

... Ti of is the (m + n − i) × (m + n − 2i)-

... Ti of is the (m + n − i) × (m + n − 2i)-

**submatrix**of S which is obtained by removing the last i rows of zeros in the**submatrix**of the columns 1 to n-i and n+1 to m+n-i of S (that is ... Its coefficient of degree j is the determinant of the square**submatrix**of Ti consisting in its m + n - 2i - 1 first rows and the (m + n - i - j)-th row ...Main Site Subjects

Related Phrases

Related Words