Title stata.com cholesky ( ) — Cholesky square-root decomposition Syntax Description Remarks and examples Conformability Diagnostics Reference Also see Syntax

numeric matrix cholesky(numeric matrix A) void cholesky(numeric matrix A) Description cholesky(A) returns the Cholesky decomposition G of symmetric (Hermitian), positive-definite matrix A. cholesky() returns a lower-triangular matrix of missing values if A is not positive definite. cholesky(A) does the same thing, except that it overwrites A with the Cholesky result. Remarks and examples stata.com The Cholesky decomposition G of a symmetric, positive-definite matrix A is A = GG′ where G is lower triangular. When A is complex, A must be Hermitian, and G′, of course, is the conjugate transpose of G. Decomposition is performed via [M-1] LAPACK. Conformability cholesky(A): A: n × n result: n × n cholesky(A): input: A: n × n output: A: n × n Diagnostics cholesky() returns a lower-triangular matrix of missing values if A contains missing values or if A is not positive definite. 1 2 cholesky ( ) — Cholesky square-root decomposition cholesky(A) overwrites A with a lower-triangular matrix of missing values if A contains missing values or if A is not positive definite. Both functions use the elements from the lower triangle of A without checking whether A is symmetric or, in the complex case, Hermitian. André-Louis Cholesky (1875–1918) was born near Bordeaux in France. He studied at the Ecole Polytechnique and then joined the French army. Cholesky served in Tunisia and Algeria and then worked in the Geodesic Section of the Army Geographic Service, where he invented his now-famous method. In the war of 1914–1918, he served in the Vosges and in Romania but after return to the Western front was fatally wounded. Cholesky’s method was written up posthumously by one of his fellow officers but attracted little attention until the 1940s