Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
M-matrix
open-in-new
<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, especially <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a>, an <i>M</i>-matrix is a matrix whose off-diagonal entries are less than or equal to zero (i.e., it is a <a href="/facts/Z-matrix_(mathematics)/csw92uKY"><i>Z</i>-matrix</a>) and whose <a href="/facts/Eigenvalue/8TjEoT8u">eigenvalues</a> have nonnegative <a href="/facts/Complex_number/2w7mqI7e">real parts</a>. The set of non-singular <i>M</i>-matrices are a subset of the class of <a href="/facts/P-matrix/XVgLSEbf"><i>P</i>-matrices</a>, and also of the class of <a href="/facts/Inverse-positive_matrix/p0Re6481">inverse-positive matrices</a> (i.e. matrices with inverses belonging to the class of <a href="/facts/Nonnegative_matrix/mYyav2eJ">positive matrices</a>). The name <i>M</i>-matrix was seemingly originally chosen by <a href="/facts/Alexander_Ostrowski/r45sj25p">Alexander Ostrowski</a> in reference to <a href="/facts/Hermann_Minkowski/tlKrpw69">Hermann Minkowski</a>, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive. </p>