How Do You Spell DIAGONALISE?

Pronunciation: [da͡ɪˈaɡənəlˌa͡ɪz] (IPA)

The word "diagonalise" is spelled with the /dʌɪˈæɡənəˌlaɪz/ phonetic transcription. The stress falls on the second syllable in this word. The 'd' in diagonalise is pronounced as a voiced dental fricative, and the 'g' is pronounced as a voiced velar plosive. The 'i' in the word is pronounced as a long vowel sound 'aɪ', and the 'a' is pronounced as an open mid-central vowel 'ə'. The suffix '-ise' means 'to make', which is used to indicate a process of turning something into a diagonal shape or position.

DIAGONALISE Meaning and Definition

1. To diagonalise refers to the process of transforming a given matrix into a diagonal matrix by applying a series of operations. In linear algebra, this technique is primarily used to simplify calculations and better understand the properties of matrices.

   Diagonalisation involves finding a matrix that is similar to the original matrix and whose elements, except for those on the main diagonal, are all zero. The process typically involves finding eigenvalues and eigenvectors of the matrix, which provide crucial information about its diagonalising potential.

   To diagonalise a matrix, the first step involves determining the eigenvalues by solving the characteristic equation of the matrix. Once the eigenvalues are obtained, the corresponding eigenvectors are computed. These eigenvectors are then arranged as columns of a matrix, which is known as the matrix of eigenvectors.

   Next, using the matrix of eigenvectors, a similarity transformation is performed, involving multiplying the inverse of the matrix of eigenvectors by the original matrix and then multiplying the result by the matrix of eigenvectors itself. This process yields a diagonal matrix, which has the eigenvalues of the original matrix on its main diagonal.

   Diagonalisation is a valuable tool in various fields, including physics, economics, and computer science. It helps in solving systems of linear differential equations, understanding the behavior of dynamical systems, simplifying matrix calculations, and analyzing quadratic forms.

Common Misspellings for DIAGONALISE

• siagonalise
• xiagonalise
• ciagonalise
• fiagonalise
• riagonalise
• eiagonalise
• duagonalise
• djagonalise
• dkagonalise
• doagonalise
• d9agonalise
• d8agonalise
• dizgonalise
• disgonalise
• diwgonalise
• diqgonalise
• diafonalise
• diavonalise
• diabonalise

Etymology of DIAGONALISE

The word "diagonalise" has its roots in mathematics. It is derived from the term "diagonal", which comes from the Latin word "diagonus", and the suffix "-ize", which is derived from the Greek suffix "-izo" meaning "to make" or "to become".

In mathematics, the process of diagonalisation refers to transforming a square matrix into a diagonal matrix through a specific procedure. The word "diagonalise" emerged in the early 20th century to describe this operation. It is commonly used in linear algebra and matrix theory.

Similar spelling words for DIAGONALISE

• diagonalize,
• diagonal,
• diagonally,
• diagonalwise,
• Tokenless,
• diagonals,
• diagonalizable.

Conjugate verb Diagonalise

CONDITIONAL

I would diagonalise

you would diagonalise

he/she/it would diagonalise

we would diagonalise

they would diagonalise

CONDITIONAL CONTINUOUS

I would be diagonalising

you would be diagonalising

he/she/it would be diagonalising

we would be diagonalising

they would be diagonalising

CONDITIONAL PERFECT

I would have diagonalise

you would have diagonalise

he/she/it would have diagonalise

we would have diagonalise

they would have diagonalise

CONDITIONAL PERFECT CONTINUOUS

I would have been diagonalising

you would have been diagonalising

he/she/it would have been diagonalising

we would have been diagonalising

they would have been diagonalising

FUTURE

I will diagonalise

you will diagonalise

he/she/it will diagonalise

we will diagonalise

they will diagonalise

FUTURE CONTINUOUS

I will be diagonalising

you will be diagonalising

he/she/it will be diagonalising

we will be diagonalising

they will be diagonalising

FUTURE PERFECT

I will have diagonalised

you will have diagonalised

he/she/it will have diagonalised

we will have diagonalised

they will have diagonalised

FUTURE PERFECT CONTINUOUS

I will have been diagonalising

you will have been diagonalising

he/she/it will have been diagonalising

we will have been diagonalising

they will have been diagonalising

IMPERATIVE

you diagonalise

we let´s diagonalise

NONFINITE VERB FORMS

to diagonalise

PAST

I diagonalised

you diagonalised

he/she/it diagonalised

we diagonalised

they diagonalised

PAST CONTINUOUS

I was diagonalising

you were diagonalising

he/she/it was diagonalising

we were diagonalising

they were diagonalising

PAST PARTICIPLE

diagonalised

PAST PERFECT

I had diagonalised

you had diagonalised

he/she/it had diagonalised

we had diagonalised

they had diagonalised

PAST PERFECT CONTINUOUS

I had been diagonalising

you had been diagonalising

he/she/it had been diagonalising

we had been diagonalising

they had been diagonalising

PRESENT

I diagonalise

you diagonalise

he/she/it diagonalises

we diagonalise

they diagonalise

PRESENT CONTINUOUS

I am diagonalising

you are diagonalising

he/she/it is diagonalising

we are diagonalising

they are diagonalising

PRESENT PARTICIPLE

diagonalising

PRESENT PERFECT

I have diagonalised

you have diagonalised

he/she/it has diagonalised

we have diagonalised

they have diagonalised

PRESENT PERFECT CONTINUOUS

I have been diagonalising

you have been diagonalising

he/she/it has been diagonalising

we have been diagonalising

they have been diagonalising