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Al-Jabr (Arabic: الجبر), also known as The Compendious Book on Calculation by Completion and Balancing (Arabic: الكتاب المختصر في حساب الجبر والمقابلة, al-Kitāb al-Mukhtaṣar fī Ḥisāb al-Jabr wal-Muqābalah; [b] or Latin: Liber Algebræ et Almucabola), is an Arabic mathematical treatise on algebra written in Baghdad around 820 by the Persian polymath ...
The algebraic equation + + = describes a sphere at the origin with a radius of 1. One application, found in geometry, is the use of algebraic statements to describe geometric figures. For example, the equation y = 3 x − 7 {\displaystyle y=3x-7} describes a line in two-dimensional space while the equation x 2 + y 2 + z 2 = 1 {\displaystyle x ...
where v 1, v 2, ..., v k are in S, and a 1, a 2, ..., a k are in F form a linear subspace called the span of S. The span of S is also the intersection of all linear subspaces containing S. In other words, it is the smallest (for the inclusion relation) linear subspace containing S. A set of vectors is linearly independent if none is in the span ...