Search results
Results from the WOW.Com Content Network
The lambdas are the eigenvalues of the matrix; they need not be distinct. In linear algebra, a Jordan normal form, also known as a Jordan canonical form, [1][2] is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis.
A matrix with all entries equal to one. a ij = 1. Pascal matrix: A matrix containing the entries of Pascal's triangle. Pauli matrices: A set of three 2 × 2 complex Hermitian and unitary matrices. When combined with the I 2 identity matrix, they form an orthogonal basis for the 2 × 2 complex Hermitian matrices. Redheffer matrix
In linear algebra, the adjugate of a square matrix A is the transpose of its cofactor matrix and is denoted by adj (A). [1][2] It is also occasionally known as adjunct matrix, [3][4] or "adjoint", [5] though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose.
Mathematical joke. A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. The humor may come from a pun, or from a double meaning of a mathematical term, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author John Allen Paulos in his book Mathematics ...
Any block diagonal matrix whose blocks are Jordan blocks is called a Jordan matrix. This (n1 + ⋯ + nr) × (n1 + ⋯ + nr) square matrix, consisting of r diagonal blocks, can be compactly indicated as or , where the i -th Jordan block is Jλi,ni. For example, the matrix is a 10 × 10 Jordan matrix with a 3 × 3 block with eigenvalue 0, two 2 ...
Matrix of ones. In mathematics, a matrix of ones or all-ones matrix has every entry equal to one. [1] Examples of standard notation are given below: Some sources call the all-ones matrix the unit matrix, [2] but that term may also refer to the identity matrix, a different type of matrix. A vector of ones or all-ones vector is matrix of ones ...
One barn is equal to 1.0 × 10 −28 m 2. The name derives from the folk expressions "As big as a barn," and "Couldn't hit the broad side of a barn", used by particle accelerator physicists to refer to the probability of achieving a collision between particles. For nuclear purposes, 1.0 × 10 −28 m 2 is actually rather large. [26]
The binomial approximation is useful for approximately calculating powers of sums of 1 and a small number x. It states that. It is valid when and where and may be real or complex numbers. The benefit of this approximation is that is converted from an exponent to a multiplicative factor. This can greatly simplify mathematical expressions (as in ...