How this calculation works
Classify a symmetric matrix according to the sign of its quadratic form.
Test the determinant and diagonal signs for a real symmetric two-by-two matrixA worked example
The matrix with diagonal 2 and off-diagonal 1 has determinant 3 and is positive definite.
Good to know
Decisions near a zero determinant are sensitive to rounding.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Classify a symmetric matrix according to the sign of its quadratic form.
The primary result is labeled “Classification”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Decisions near a zero determinant are sensitive to rounding.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
The matrix with diagonal 2 and off-diagonal 1 has determinant 3 and is positive definite.
Which rule does this calculator apply?
Test the determinant and diagonal signs for a real symmetric two-by-two matrix