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Lace is a delicate fabric made of yarn or thread in an open weblike pattern, made by machine or by hand. Generally, lace is divided into two main categories, needlelace and bobbin lace, although there are other types of lace, such as knitted or crocheted lace. Other laces such as these are considered as a category of their specific craft. Knitted lace, therefore, is an example of knitting. This article considers both needle lace and bobbin lace.
Bobbin lace is a lace textile made by braiding and twisting lengths of thread, which are wound on bobbins to manage them. As the work progresses, the weaving is held in place with pins set in a lace pillow, the placement of the pins usually determined by a pattern or pricking pinned on the pillow. Bobbin lace is also known as pillow lace, because it was worked on a pillow, and bone lace, because early bobbins were made of bone or ivory. Bobbin lace is one of the two major categories of handmade laces, the other being needle lace, derived from earlier cutwork and reticella.
In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector where is the transpose of . More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector where denotes the conjugate transpose of Positive semi-definite matrices are defined similarly, except that the scalars and are required to be positive or zero (that is, nonnegative).
In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is to that of projective modules.
In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every non-zero vector of V. According to that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the same way, except that "always positive" and "always negative" are replaced by "never negative" and "never positive", respectively.