Matrix chain multiplication (or the matrix chain ordering problem) is an optimization problem concerning the most efficient way to multiply a given sequence...

Because matrix multiplication is such a central operation in many numerical algorithms, much work has been invested in making matrix multiplication algorithms...

in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns...

complexity of matrix multiplication dictates how quickly the operation of matrix multiplication can be performed. Matrix multiplication algorithms are a central...

multiplications needed to multiply a chain of matrices from matrix i to matrix j (i.e. Ai × .... × Aj, i.e. i<=j). We split the chain at some matrix k...

multiplication. Most commonly, a matrix over a field F {\displaystyle F} is a rectangular array of elements of ⁠ F {\displaystyle F} ⁠. A real matrix...

In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number...

Jacobian determinant, and the multiplicative inverse of the derivative is replaced by the inverse of the Jacobian matrix. The Jacobian determinant is fundamentally...

except the commutative law of multiplication (a familiar example of such a noncommutative multiplication is matrix multiplication). From this all of the rules...

this is O ( log k ⁡ n ) {\displaystyle O(\log ^{k}n)} . For example, matrix chain ordering can be solved in polylogarithmic time on a parallel random-access...

graphs,[AH73] minimum routing cost spanning trees,[H74] and the matrix chain multiplication problem.[HS82] Hu's family came from Zhejiang. Hu was born in...

of associating n applications of a binary operator, as in the matrix chain multiplication problem). For n = 3, for example, we have the following five...

In calculus, the chain rule is a formula that expresses the derivative of the composition of two differentiable functions f and g in terms of the derivatives...

square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or |A|. Its value characterizes some properties of the matrix and the...

otherwise; this is the adjacency matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed...

In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function...

algorithms) matched edge matched vertex matching (graph theory) matrix matrix-chain multiplication problem max-heap property maximal independent set maximally...

called addition and multiplication, which obey the same basic laws as addition and multiplication of integers, except that multiplication in a ring does not...

The overall network is a combination of function composition and matrix multiplication: g ( x ) := f L ( W L f L − 1 ( W L − 1 ⋯ f 1 ( W 1 x ) ⋯ ) ) {\displaystyle...

such a way that quaternion addition and multiplication correspond to matrix addition and matrix multiplication. One is to use 2 × 2 complex matrices, and...

the matrix multiplication A v = λ v , {\displaystyle A\mathbf {v} =\lambda \mathbf {v} ,} where the eigenvector v is an n by 1 matrix. For a matrix, eigenvalues...

{\displaystyle {\begin{matrix}H_{1}(a,b)=a+b=&a+\underbrace {1+1+\dots +1} \\&b{\mbox{ copies of }}1\end{matrix}}} Multiplication by a natural number is...

In mathematics, a Carleman matrix is a matrix used to convert function composition into matrix multiplication. It is often used in iteration theory to...

depends on the order of the factors. Matrix multiplication, for example, is non-commutative, and so is multiplication in other algebras in general as well...

probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})} of nonnegative...

can be performed on square matrices are matrix addition, multiplication by a scalar, and matrix multiplication. These are exactly those operations necessary...

Markov chain Unistochastic matrix — a doubly stochastic matrix whose entries are the squares of the absolute values of the entries of some unitary matrix The...

vector generates the chain via multiplication by ⁠ A − λ I {\displaystyle A-\lambda I} ⁠. Therefore, the statement that every square matrix A can be put in...

When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: b n...

a matrix decomposition of the original matrix. The elementary row operations may be viewed as the multiplication on the left of the original matrix by...