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In mathematics, a unimodular matrix ''M'' is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over the integers: there is an integer matrix ''N'' which is its inverse (these are equivalent under Cramer's rule). Thus every equation ''Mx'' = ''b'', where ''M'' and ''b'' are both integer, and ''M'' is unimodular, has an integer solution. The unimodular matrices of order ''n'' form a group, which is denoted . ==Examples of unimodular matrices== Unimodular matrices form a subgroup of the general linear group under matrix multiplication, i.e. the following matrices are unimodular: * Identity matrix * The inverse of a unimodular matrix * The product of two unimodular matrices Further: * The Kronecker product of two unimodular matrices is also unimodular. This follows since : : where ''p'' and ''q'' are the dimensions of ''A'' and ''B'', respectively. Concrete examples include: * Pascal matrices * Permutation matrices * the three transformation matrices in the ternary tree of primitive Pythagorean triples 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「unimodular matrix」の詳細全文を読む スポンサード リンク
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