Noun
/bloʊk stəˈkæs.tɪk ˈmeɪ.trɪks/
A block-stochastic matrix is a specific type of matrix that is used in linear algebra and probability theory. It is partitioned into blocks, where each block is a stochastic matrix. A stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each entry is a non-negative real number, and the sum of the entries in each row (or column, depending on the context) equals one. Block-stochastic matrices are often utilized in areas such as statistics, machine learning, and complex systems analysis.
Frequency of Use: The term is primarily used in written contexts, such as academic papers, textbooks, and technical articles. It is less common in everyday oral speech unless the discussion pertains to advanced mathematics or related fields.
A block-stochastic matrix allows for the modeling of Markov processes at different levels of granularity.
Un bloque-matriz estocástica permite la modelización de procesos de Markov en diferentes niveles de granularidad.
In certain applications, a block-stochastic matrix can simplify the computation of state transitions.
En ciertas aplicaciones, una bloque-matriz estocástica puede simplificar el cálculo de las transiciones de estado.
Researchers have developed algorithms that efficiently manipulate block-stochastic matrices.
Los investigadores han desarrollado algoritmos que manipulan de manera eficiente las matrices bloque-estocásticas.
While "block-stochastic matrix" does not frequently appear in idiomatic expressions, the concept of "stochastic" does play a significant role in several academic and technical phrases. Below are a few applications and phrases related to stochastic processes:
"The stochastic nature of the model introduces variability in outcomes."
La naturaleza estocástica del modelo introduce variabilidad en los resultados.
"Understanding the stochastic process is essential for accurate prediction."
Entender el proceso estocástico es esencial para una predicción precisa.
"In stochastic simulations, randomness can lead to unexpected results."
En simulaciones estocásticas, la aleatoriedad puede conducir a resultados inesperados.
The term "block-stochastic matrix" combines three parts: - "Block" comes from the Old French bloc, meaning a solid piece of material. - "Stochastic" derives from the Greek stokhastikos, meaning probabilistic or conjectural. - "Matrix" comes from the Latin matrix, which means 'womb' or 'source', and in mathematics, denotes an array of numbers set out by rows and columns.
Synonyms: - Partitioned stochastic matrix - Composite stochastic matrix
Antonyms: - Deterministic matrix - Non-stochastic matrix
This comprehensive overview provides clarity on the concept of a block-stochastic matrix, along with its usage, examples, idiomatic expressions related to stochastic processes, etymology, and synonyms/antonyms.