Principal Submatrix

A principal submatrix of a square matrix is a submatrix obtained by selecting the same index set for its rows and columns, retaining their original order. It is denoted , or simply (Horn and Johnson 2013, p. 17).

The selected indices need not be consecutive. For example, selecting rows 1 and 3 and columns 1 and 3 of a matrix gives

$A[{1,3}]=[a_(11) a_(13); a_(31) a_(33)].$

A principal submatrix is necessarily a square matrix, but a square submatrix need not be principal because its row and column index sets may differ.

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References

Horn, R. A. and Johnson, C. R. "Submatrices." §0.7.1 in Matrix Analysis, 2nd ed. New York: Cambridge University Press, p. 17, 2013.

Cite this as:

Weisstein, Eric W. "Principal Submatrix." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PrincipalSubmatrix.html

Principal Submatrix

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