positive definite
All eigenvalues positive
Positive definite describes a matrix or quadratic form with a specific mathematical property: when multiplied by any nonzero vector and its transpose, the result is always a positive number.
A positive definite matrix has all positive eigenvalues and represents surfaces that curve upward in every direction, like a bowl.
The concept appears throughout linear algebra, statistics, and optimization, where positive definite matrices guarantee unique solutions and stable computations.
The covariance matrix must be positive definite for the model to work.
Ordered numerical arrangement
- eigenvaluesTransformation scaling constants
- symmetricEqual on both sides
- determinantMatrix-derived scalar quantity
- spectrumContinuous range of values
linear algebra · definiteness · convexity · optimization · factorization · orthogonal · diagonal · inverse
State of balance
- convergenceProcess of approaching sameness
- boundednessState of having limits
- asymptoticApproaching a limit infinitely
- feedbackReturned response data
robust · damping · trajectory · attractor · basin · perturbation
matrix
Ordered numerical arrangement
- eigenvaluesTransformation scaling constants
- symmetricEqual on both sides
- determinantMatrix-derived scalar quantity
spectrum · linear algebra · definiteness · convexity · optimization · factorization · orthogonal · diagonal · inverse · trace
equilibrium
State of balance
- convergenceProcess of approaching sameness
- boundednessState of having limits
- asymptoticApproaching a limit infinitely
feedback · robust · damping · trajectory · attractor · basin · perturbation
- linear algebramatrix, linear equation, vectors, linear function, matrices
- bilinear formsdiscriminant, signature, orthogonality, isotropic, anisotropic
- optimizationoptimization, caching, optimum, indexing, prefetching
- matricestranspose, determinants, rows, cells, Hermitian matrices
- eigenvalueseigenvalue, eigenvector, eigenvalues, eigenvectors, eigendecomposition