block-stochastic matrix - meaning, definition, translation, pronunciation
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block-stochastic matrix (english) - meaning, definition, translation, pronunciation


Part of Speech

Noun

Phonetic Transcription

/bloʊk stəˈkæs.tɪk ˈmeɪ.trɪks/

Meaning and Usage

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.

Example Sentences

Idiomatic Expressions

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:

Etymology

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 and Antonyms

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.



25-07-2024