SPSS: "this matrix is not positive definite"
SPSS shows this in factor analysis (and reliability) when your correlation matrix has a zero or negative eigenvalue, so it cannot be factored. The usual causes are reverse-worded items that were never recoded, redundant or collinear items, pairwise handling of missing data, or a sample smaller than the number of variables.
What the error means
SPSS factor analysis needs a correlation matrix that is positive definite — one with all positive eigenvalues and a non-zero determinant. When it is not, SPSS reports "this matrix is not positive definite" and may refuse to extract factors or to compute KMO and Bartlett's test. It is the same underlying issue as a non-positive-definite covariance matrix, seen through SPSS's factor-analysis dialog.
Common causes
- Reverse-worded items not recoded, so some correlations point the wrong way.
- Redundant items — two near-identical questions, or a total/sum entered alongside the items that make it up.
- Multicollinearity: items that are almost perfectly correlated.
- Pairwise deletion of missing values, which can build an inconsistent matrix (a correlation can come out above 1).
- Sample size at or below the number of variables, making the matrix singular.
- Including constant or near-constant items (almost no variance).
How to fix it
- Open the correlation matrix in the output (tick "Coefficients" and "Determinant" under Descriptives). A determinant at or near 0 confirms the problem.
- Recode reverse-scored items with Transform > Recode into Different Variables, then re-run.
- Remove redundant items: drop one of any near-duplicate pair and never include a composite score with its component items.
- Switch missing-value handling to Exclude cases listwise instead of pairwise.
- Check that N is larger than the number of variables — ideally several times larger — and collect more data if needed.
- Drop any item with near-zero variance, then re-run the factor analysis.
How to avoid it next time
Recode reverse items and screen for duplicates before you run factor analysis, use listwise deletion, and size the sample well above the item count. Explonia computes the correlation matrix and reliability as you build the study and flags items that overlap heavily, so you can catch a near-singular matrix before it blocks the analysis. See the EFA and reliability methods, and sample size.
Frequently asked questions
Why does SPSS say the determinant is zero?
A zero (or near-zero) determinant is how SPSS signals a non-positive-definite correlation matrix: at least one variable is a near-linear combination of others, usually from redundant items, perfect multicollinearity, or unrecoded reverse items. Remove the redundancy or recode the items and the determinant should become positive.
Will recoding reverse items really fix it?
Often, yes — if some items were reverse-worded and never recoded, part of the matrix has the wrong sign, which can make it non-positive-definite. Recode them so every item points the same direction and re-run; if the message persists, look for redundant items or a too-small sample.
Can pairwise missing-data handling cause this?
Yes. Pairwise deletion computes each correlation on a different subset of cases, which can produce an internally inconsistent matrix (even a correlation above 1). Switching to listwise deletion, or using a principled missing-data method, often resolves it.
How to cite this page
If this page helped your research, you can cite it (APA 7):
Szymkowiak, A. (2026). SPSS: This Matrix Is Not Positive Definite (Fix). Explonia. https://explonia.com/fix/spss-matrix-not-positive-definite/
Last updated: July 2026
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