positievedefiniete
positievedefiniete refers to a property of certain mathematical objects, most notably square matrices and quadratic forms. A real symmetric matrix is called positive-definite if for any non-zero vector x, the quadratic form xᵀAx is strictly positive. Here, xᵀ denotes the transpose of vector x, and Ax is the matrix-vector product. This condition implies that all eigenvalues of the matrix A are strictly positive. Equivalently, a matrix is positive-definite if and only if all its leading principal minors are strictly positive.
In the context of quadratic forms, a function q(x) = xᵀAx is positive-definite if q(x) > 0 for
The concept can also be extended to complex Hermitian matrices, where the condition becomes xᴴAx > 0