"Diagonalise" Pronounce,Meaning And Examples

"Diagonalise" Natural Recordings by Native Speakers

Diagonalise

"Diagonalise" Meaning

To diagonalize means to transform a matrix into a diagonal matrix, where all the non-diagonal elements are zero, and the diagonal elements are non-zero. It is often used in linear algebra and matrix theory to simplify the representation of a matrix.

"Diagonalise" Examples

Examples of "Diagonalise"

Mathematics

The matrix can be diagonalised using the eigenvectors of the matrix, leading to a simpler form for solving the equation. [1]
In linear algebra, a matrix is said to be diagonalisable if it is similar to a diagonal matrix, and this can be done by finding the eigenvectors and eigenvalues of the matrix. [2]

Linguistics

The grammatical structure of the sentence is diagonalised, with the subject acting as an object, and the verb taking on a new meaning. [3]
The poet's use of imagery diagonalises the reader, creating a sense of disorientation and confusion. [4]

Sports

In this corner, our agility specialist will diagonalise the defender's line, creating an open passing lane for the midfielder. [5]
The coach will diagonalise their opponent's formation by sending in a substitute who can exploit the space left open. [6]

Please note that the word "diagonalise" is primarily used in mathematical and scientific contexts, although it can also be used metaphorically to describe the manipulation of structures or systems in other fields.

"Diagonalise" Similar Words

Diagnosticity

Diagnostics

Diagnozed

Diagnosed is the past tense of the verb "diagnose", which means to identify or determine the nature and cause of a disease or medical condition, typically through medical examination and testing.

Diagnozing

Diagometer

Diagonal

The word "diagonal" refers to a line or shape that intersects two other lines or edges at an angle other than a right angle. It can also refer to a diagonal move or action, such as a diagonal crossing of a room or a diagonal cut in a material. In a broader sense, the term "diagonal" can also be used to describe a line or direction that is slanting or at an angle, rather than vertical or horizontal.

Diagonalisable

Diagonalisation

Diagonalisation is a term used in mathematics, particularly in linear algebra and differential equations. It refers to the process of transforming a matrix (a table of numbers) into a diagonal matrix, where all non-zero entries are located along the main diagonal from top-left to bottom-right.<br><br>In other words, diagonalisation involves finding a way to rewrite a matrix as a combination of its eigenvalues (numbers that, when multiplied by the original matrix, produce a scaled version of itself) and its eigenvectors (non-zero vectors that, when multiplied by the original matrix, result in a scaled version of itself). This is often achieved through a series of mathematical operations, such as matrix multiplication and exponentiation.<br><br>Diagonalisation has many practical applications in fields like physics, engineering, and computer science, where it is used to solve systems of linear equations, determine the stability of differential equations, and perform statistical analysis.

Diagonality

Diagonalizable

Diagonalization

Diagonalization is a mathematical process or technique used to express a matrix or a linear operator in a diagonal form. In linear algebra, it is a method of transforming a square matrix into a diagonal matrix, where non-zero elements are only on the main diagonal and the rest of the matrix is zero. This is often used to solve systems of linear equations, find eigenvalues and eigenvectors, and calculate determinants.

Diagonalize

Diagonally

Diagonally refers to something that is sloping or crossing at an angle, rather than horizontally or vertically. It can be used to describe the direction of a line, a movement, or even the way something is arranged or placed. For example: "The stairs were built diagonally across the front of the building", or "She walked diagonally across the room to get to the other side". In a mathematical sense, a diagonal is an imaginary line that connects two non-adjacent corners of a rectangle or square.