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Term: Diagonalise

Description:

Diagonalise is a mathematical term used in linear algebra to describe the process of transforming a matrix into a diagonal matrix. It involves finding a matrix that has the same eigenvectors as the original matrix. This technique is essential in various mathematical and scientific applications, such as solving systems of linear differential equations and optimizing eigenvalue problems.

Sample Sentences:

Verb (Transitive):

1. To diagonalise a square matrix, you need to find its eigenvalues and eigenvectors first.
2. The mathematician used complex algorithms to diagonalise the large matrix, simplifying the subsequent calculations.

Verb (Intransitive):

1. The matrix diagonalises easily due to its symmetric properties.
2. We studied how certain matrices diagonalise more readily than others in our linear algebra class.

Related Products:

• Linear Algebra Textbooks
• Matrix Algorithms