diagonalize

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Definitions from WordNet

Verb diagonalize has 1 sense

diagonalize, diagonalise - transform a matrix to a diagonal matrix
--₁ is one way to translate, transform

Derived forms: noun diagonalization₁, noun diagonal₄
Sample sentence:
Somebody ----s something

Definitions from the Web

Term: diagonalize Description: Diagonalize, in the context of linear algebra, refers to the process of finding a diagonal matrix that is similar to a given matrix. It involves finding a matrix P such that P⁻¹AP is a diagonal matrix.

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Matrix Calculator Sense 1 (Verb): - When used as a verb, diagonalize means to convert a given matrix into a diagonal matrix by using a similarity transformation.

Example Sentence: To solve the system of linear equations, we first need to diagonalize the coefficient matrix.
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Sense 2 (Verb): - Diagonalize can also mean finding a set of orthogonal eigenvectors for a given matrix, creating a diagonal matrix with eigenvalues as its diagonal entries.

Example Sentence: In order to calculate the determinant, we need to diagonalize the matrix first.
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Sense 3 (Adjective): - As an adjective, diagonalize can refer to a property or characteristic of a matrix being diagonalizable.

Example Sentence: The eigenvalues of a symmetric matrix are always real, making it diagonalizable.
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Sense 4 (Noun): - Diagonalize can also be used as a noun to represent the act or process of diagonalizing a matrix.

Example Sentence: The diagonalization of the matrix was completed by applying the appropriate transformation.
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