MaplePrimes - comments on Post, program to decide when a matrix is symmetric positive definite????

MaplePrimes - comments on Post, program to decide when a matrix is symmetric positive definite???? http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Wed, 10 Jun 2026 18:59:25 GMT Wed, 10 Jun 2026 18:59:25 GMT The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? http://www.mapleprimes.com/images/mapleprimeswhite.jpg MaplePrimes - comments on Post, program to decide when a matrix is symmetric positive definite???? http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric built in command http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment79917 Maple can check for positive definite using the IsDefinite command from the LinearAlgebra package. The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 79917 Wed, 26 Apr 2006 20:06:55 Z dharr dharr If you really want to do it yourself ... http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment86527 Check for "cholesky algorithm" in a textbook covering numerical linear algebra. Its implementation is rather straightforward. Regards WW The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 86527 Mon, 01 May 2006 21:01:11 Z Werner Werner Does it have to be symmetric? http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment81731 Maple 12 / help states this: LinearAlgebra[IsDefinite] - test for positive or negative definite or indefinite Matrices Description The IsDefinite(A, query = 'positive_definite') returns true if A is a real symmetric or a complex Hermitian Matrix and all the eigenvalues are determined to be positive. Because the default query is query = 'positive_definite', this command is equivalent to IsDefinite(A). This description doesn't imply that IsDefinite(A) will always give true when matrix A is positive definite and not symmetric. Question: Is it just a bug in help description or we can't rely on function IsDefinite() for non symmetric matrices? (I didn't find a counterexample, i.e. a non symmetric positive definite matrix A for which IsDefinite(A) = false) The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 81731 Sun, 07 Mar 2010 17:07:24 Z Robertas Vilkas Robertas Vilkas Non-symmetric http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment94378 For example, for a 2 x 2 matrix: <pre> > with(LinearAlgebra):    M:= <<1 | 0>, <3 | 1>>;    Eigenvalues(M); </pre> [   1   ] [   1   ] <pre> > IsDefinite(M); </pre> false The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 94378 Mon, 08 Mar 2010 01:50:00 Z Robert Israel Robert Israel help bug http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment94379 It's a bug in the documentation only, I think, that it doesn't describe the nonsymmetric case. The term "positive definite" refers to what sign the scalar value x^%T.A.x can take on for any nonzero column Vector x, rather than (always) what sign the eigenvalues have. Hence Robert's example below is not a counter-example to match your bracketed/ie description, I think. Now, some texts state the definition of the term "positive definite" by stating that "A symmetric/hermitian matrix is positive-definite if..." and so of course with that wording the symmetric aspect is built right into the concept. And for a symmetric/hermitian Matrix the positive-definiteness matches whether the eigenvalues are all positive. But the definition needn't be taken as always including the symmetric quality. Modulo bugs, you ought to be able to rely on IsDefinite for nonsymmetric Matrices. Having said that, I sort of remember that there was a short-lived (1 release, then fixed, maybe in Maple 12?) glitch introduced in the recent past for the nonsymmetric case. It's Sunday afternoon,... and I hope that I haven't remembered that situation all wrong. acer The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 94379 Mon, 08 Mar 2010 03:08:18 Z acer acer positive definite http://www.mapleprimes.com/posts/42914-Program-To-Decide-When-A-Matrix-Is-Symmetric?ref=Feed:MaplePrimes:program to decide when a matrix is symmetric positive definite????:Comments#comment94380 There are, I think, various different definitions of "positive definite" that all coincide in the hermitian case, but don't in general.  It appears to me that IsDefinite(A) actually works on A + A^%H, so (for real matrices) if you use the criterion that x^%T . A . x > 0 for all nonzero real vectors x,  IsDefinite should give a correct answer. The latest comments added to the Post, program to decide when a matrix is symmetric positive definite???? 94380 Mon, 08 Mar 2010 06:20:25 Z Robert Israel Robert Israel