A Gaussian process require the eigenvalues of the correlation matrix being non-negative. I wrote an attached code, that allows you perform this procedure into R. This procedure is described in the following paper:
dos Santos, J. P. R. 2016 - Inclusion of dominance effects in the multivariate GBLUP model
This paper is available in my research gate (any doubts, I am the first author and you can contact me here).
Bear in mind that the general advise is that sample size should be greater than one hundred for performing factor analysis. You should acknowledge this as a limitation of your design.
Velicer, W. F., et al. (2000). Chapter 3: Construct explication through factor or component analysis: A review and evaluation of alternative procedures for determinng the number of factors or components. Problems and Solutions in Human Assessment: Honoring Douglas N. Jackson at Seventy. R. D. Goffin and E. Helmes. New York, Springer-Verlag: 41-71.
As Pual says, you have 38 items and 50 individual. It is hard to measure. You have to collect some data. But in general if the Correlation matrix is NPD, smooting could be done.
Psych package (Revelle, 2017) in R is making the necessary smooting automatically. Maybe you can use it.