I find the following snippet unexpected. srand(1); X = rand(1000, 1000) - 0.5; (X' *X) == (X' *X)' #true (1 * X' *X) == (1 * X' *X)' #false Multiplying by 1 changes the symmetry, probably due to floating-point arithmetic issues. But I fail to understand where the failure happens. Let A = X' * X. …

I think that 1 * X' * X is evaluated as (1 * X') * X, and 1 * X' cannot be recognized as coming from the same matrix X. You should use 1 * (X' * X), or even better, Symmetric(X' * X) * c for some generic real c (I am assuming the 1 is just for the MWE).

1 * X' * X is not symmetric

General Usage

Nosferican June 5, 2018, 1:57pm 7

Those are different BLAS routines. If not mistaken syrk (symmetric rank-k update) takes advantage of crossproducts while gemm (General Matrix Multiply) is general.

Topic		Replies	Views
Product of a scalar with Symmetric is not symmetric (while Symmetric times scalar is) General Usage	4	502	September 27, 2018
Symv producing incorrect results Numerics blas	2	651	December 5, 2017
Inverse of a symmetric matrix is not symmetric? General Usage	16	3486	April 4, 2018
A symmetric matrix multiplied by a scalar is not symmetric New to Julia	2	717	April 8, 2019
Why is matrix times matrix transpose not a Symmetric / Hermitian matrix General Usage	12	1345	April 10, 2022

1 * X' * X is not symmetric

Related topics