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

improvement with the newly discovered matrix multiplication method of Alpha Evolve] Because matrix multiplication is such a central operation in many numerical...

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...

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...

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

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...

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...

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

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...

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...

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...

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...

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...

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...

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...

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

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...

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

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...

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...

for this device, which performed a 6 × 6 matrix multiplication modulo 26 using a system of gears and chains. Unfortunately the gearing arrangements (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...

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...

{\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...

channel, and matrix chain multiplication. The power of the GDL lies in the fact that it applies to situations in which additions and multiplications are generalized...

idempotent element of a matrix ring is precisely an idempotent matrix. For general rings, elements idempotent under multiplication are involved in decompositions...

basic operations of arithmetic, the other three being subtraction, multiplication, and division. The addition of two whole numbers results in the total...