Encyclopedia - Determinant: Encyclopedia Ii - Determinant - Determinants Of 2-by-2 Matrices
The 2×2 matrix has determinant . The interpretation when the matrix has real number entries is that this gives the area of the para...   » Read the article

Encyclopedia - Determinant: Encyclopedia Ii - Determinant - Applications
Determinants are used to characterize invertible matrices (namely as those matrices, and only those matrices, with non-zero determinants)...   » Read the article

Encyclopedia - Determinant: Encyclopedia Ii - Determinant - General Definition And Computation
Suppose is a square matrix. If A is a 1-by-1 matrix, then If A is a 2-by-2 matrix, then For a 3-by-3 matrix A, the formula is more com...   » Read the article

Encyclopedia - Skew-symmetric Matrix: Encyclopedia Ii - Skew-symmetric Matrix - Properties
Sums and scalar products of skew-symmetric matrices are again skew-symmetric. Hence, the skew-symmetric matrices form a vector space. If ...   » Read the article

Encyclopedia - Lorentz Group: Encyclopedia Ii - Lorentz Group - Relation To The Möbius Group
The restricted Lorentz group SO+(1, 3) is isomorphic to the Möbius group, which is, in turn, isomorphic to the projective special linear...   » Read the article

Encyclopedia - Lie Algebra: Encyclopedia Ii - Lie Algebra - Classification Of Lie Algebras
Real and complex Lie algebras can be classified to some extent, and this classification is an important step toward the classification of...   » Read the article

Encyclopedia - Orthogonal Matrix: Encyclopedia Ii - Orthogonal Matrix - Spin And Pin
A subtle technical problem afflicts some uses of orthogonal matrices. Not only are the group components with determinant +1 and −1 not ...   » Read the article

Encyclopedia - Determinant: Encyclopedia Ii - Determinant - Example
Suppose we want to compute the determinant of We can go ahead and use the Leibniz formula directly: Alternatively...   » Read the article

Encyclopedia - Determinant: Encyclopedia Ii - Determinant - Properties
The determinant is a multiplicative map in the sense that for all n-by-n matrices A and B. This is generalized by the Cauchy-Binet for...   » Read the article

Encyclopedia - Determinant: Encyclopedia Ii - Determinant - Generalizations And Related Functions
As was pointed out above, it is possible to unambiguously define the determinant of any linear map f : V → V, if V is a finite-dim...   » Read the article