Understand the subject
What does positive definite mean?
A real symmetric matrix is positive definite when every nonzero vector produces a positive quadratic form.
Use it to check an important structural condition for supported symmetric matrices.
See the structure
What the calculation is doing
v→Av = λvsame direction, scaled length
Worked interpretation
Read the result in context
positive definite ⇔ every eigenvalue > 0
Interpret with care
Important boundary
This numerical classification uses a disclosed tolerance near zero.
Use the Matrix Calculator to experiment with small exact matrix operations before applying a more specialized route.
Quick guide
How to use this calculator
- Set the matrix dimensions required by the task.
- Fill every visible entry and any operation-specific control.
- Read the result type, factors, classification, and disclosed limitations.
Calculation method
Apply the stated linear-algebra contract
Positive definite ⇔ every eigenvalue is positive
Undefined, singular, dimensionally incompatible, dependent, or unsupported inputs receive an explicit message instead of a fabricated numeric result.
Worked example
Example interpretation
Eigenvalues within the disclosed tolerance are treated as zero.
Positive definite ⇔ every eigenvalue is positive
Supported inputs
Precision and limits
Matrix size
Input matrices are limited to 1–6 rows and columns; operation-specific square, rank, or compatibility rules still apply.
Entry precision
Enter signed finite decimals with at most 30 digits and 15 decimal places.
Numerical policy
Results use real double-precision arithmetic, a 1e-10 structural tolerance where stated, bounded iterations, and labelled approximations.
