Search results
Results From The WOW.Com Content Network
Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, [2] to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra , and as such has numerous applications in many areas of mathematics, as well as in applied ...
The characteristic polynomial of a matrix A is a scalar-valued polynomial, defined by () = ().The Cayley–Hamilton theorem states that if this polynomial is viewed as a matrix polynomial and evaluated at the matrix itself, the result is the zero matrix: () =.
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices. [1] [2]Intuitively, a matrix interpreted as a block matrix can be visualized as the original matrix with a collection of horizontal and vertical lines, which break it up, or partition it, into a collection of smaller matrices.
It follows that the space of all Hamiltonian matrices is a Lie algebra, denoted sp(2n). The dimension of sp(2n) is 2n 2 + n. The corresponding Lie group is the symplectic group Sp(2n). This group consists of the symplectic matrices, those matrices A which satisfy A T JA = J. Thus, the matrix exponential of a Hamiltonian matrix is symplectic ...
In quantum mechanics, a density matrix (or density operator) is a matrix that describes an ensemble [1] of physical systems as quantum states (even if the ensemble contains only one system).
Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same.
These microduplications likely represent the predicted reciprocal rearrangements to the microdeletions characterized in the 22q11.2 region. [2] Smaller microduplications may occur within this highly dynamic with frequent rearrangements using alternative low-copy repeats as recombination substrates within and distal to the DiGeorge syndrome region.