Dodatkowe przykłady dopasowywane są do haseł w zautomatyzowany sposób - nie gwarantujemy ich poprawności.
If is a positive-definite matrix, for any real number :
A positive matrix is not the same as a positive-definite matrix.
The function on the domain of positive-definite matrices is convex.
Then, the positive elements are the positive-definite matrices.
A positive-definite matrix is a matrix with special properties.
The lower triangular matrix is the 'Cholesky triangle' of the original, positive-definite matrix.
Gaussian elimination is numerically stable for diagonally dominant or positive-definite matrices.
Positive-definite kernel, a generalization of a positive-definite matrix.
In operator theory, a branch of mathematics, a positive definite kernel is a generalization of a positive-definite matrix.
Let M be a symmetric and N a symmetric and positive-definite matrix.
The diffusion tensor, a 3 x 3 symmetric positive-definite matrix, offers a straightforward solution to both of these goals.
P are all positive-definite matrices, the problem is convex and can be readily solved using interior point methods, as done with semidefinite programming.
Since is symmetric, positive-definite matrix, it follows that all eigenvalues of satisfy , ().
However, a positive-definite matrix has precisely one positive-definite square root, which can be called its principal square root.
A sufficient matrix is a generalization both of a positive-definite matrix and of a P-matrix, whose principal minors are each positive.
Mathematically this means that the result of subtracting the expected squared error (which is not usually known) from is a semidefinite or positive-definite matrix.
In statistics, a matrix gamma distribution is a generalization of the gamma distribution to positive-definite matrices.
The Wishart distribution is a multivariate generalization of the gamma distribution (samples are positive-definite matrices rather than positive real numbers).
A symmetric, and a symmetric and positive-definite matrix can be simultaneously diagonalized, although not necessarily via a similarity transformation.
The collection of all copositive matrices is a proper cone; it includes as a subset the collection of real positive-definite matrices.
For a given pair of real symmetric positive-definite matrices, and a given non-zero vector , the generalized Rayleigh quotient is defined as:
The variance of X is a kxk symmetric positive-definite matrix V. The multivariate normal distribution is a special case of the elliptical distributions.
Where sums of squares appear in univariate analysis of variance, in multivariate analysis of variance certain positive-definite matrices appear.
(B is a Hermitian positive-definite matrix and u the conjugate transpose of u) the Pythagorean theorem is:
In statistics, the inverse Wishart distribution, also called the inverted Wishart distribution, is a probability distribution defined on real-valued positive-definite matrices.