Definite matrix: Difference between revisions

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== Further properties ==

Every positive definite matrix is invertible and its inverse is also positive definite. If ''M'' is positive definite and ''r'' > 0 is a real number, then ''rM'' is positive definite. If ''M'' and ''N'' are positive definite, then ''M + N'' is also positive definite, and if ''MN'' = ''NM'', then ''MN'' is also positive definite. To everyEvery positive definite matrix ''M'', therehas existsat preciselyleast one [[square root]]: a positive definite matrix ''N'' withsuch that ''N''² = ''M''. In fact, ''M'' may have infinitely many square roots, but exactly one positive definite square root.