Linear B is a syllabic script that was used for writing Mycenaean Greek, an early form of Greek. The script pre-dated the Greek alphabet by several centuries. A recent finding of the oldest Mycenaean writing dates to about 1450 BC. Linear B, found mainly in the palace archives at Knossos, Cydonia,Pylos, Thebes and Mycenae, disappeared with the fall of Mycenaean civilization. The succeeding period, known as the Greek Dark Ages, provides no evidence of the use of writing.

The script appears related to Linear A, an undeciphered earlier script used for writing the Minoan language, and the later Cypriot syllabary, which recorded Greek. Linear B consists of around 87 syllabic signs and a large repertory of ideographic signs. These ideograms or "signifying" signs stand for objects or commodities, but do not have phonetic value and are never used as word signs in writing a sentence.

The application of Linear B seems to have been confined to administrative contexts. In all the thousands of clay tablets, a relatively small number of different "hands" have been detected: 45 in Pylos (west coast of the Peloponnese, in southern Greece) and 66 in Knossos (Crete). From this fact it could be thought that the script was used only by a guild of professional scribes who served the central palaces. Once the palaces were destroyed, the script disappeared.

In mathematics, a linear map or linear function f(x) is a function which satisfies the following two properties:

It can be shown that additivity implies the homogeneity in all cases where α is rational; this is done by proving the case where α is a natural number by mathematical induction and then extending the result to arbitrary rational numbers. If f is assumed to be continuous as well then this can be extended to show that homogeneity for α any real number, using the fact that rationals form a dense subset of the reals.

In this definition, x is not necessarily a real number, but can in general be a member of any vector space. A less restrictive definition of linear function, not coinciding with the definition of linear map, is used in elementary mathematics.

The concept of linearity can be extended to linear operators. Important examples of linear operators include the derivative considered as a differential operator, and many constructed from it, such as del and the Laplacian. When a differential equation can be expressed in linear form, it is particularly easy to solve by breaking the equation up into smaller pieces, solving each of those pieces, and adding the solutions up.