diagonalizable

9.9

A matrix you can change into one with numbers only on the main diagonal and zeros elsewhere

adjective
/daɪəˈɡɒnəlˌaɪzəbl/

Specialized

: diagonalizable

A square matrix is diagonalizable when it has enough independent eigenvectors to form a basis.

Examples

In general, not all matrices are diagonalizable first of all, so.
So you need for simultaneously diagonalizable that you need that S&P commute.
The matrix is diagonalizable if it can be transformed into a diagonal form for easier computation.
To solve the system of equations, we first check if the matrix is diagonalizable by finding its eigenvalues.

Surface Forms

diagonalizable positive

diagonalizabler comparative

diagonalizablest superlative

Morphology

diagonalizable = diagonalize (transparent) = diagonal + ize + able

Standard adjectival -able added to the verb 'diagonalize', producing 'capable of being diagonalized'; the formation follows regular English morphology.

Etymology

Diagonalizable comes from diagonal, a line that goes 'across' a square from one corner to the opposite, and the ending -able meaning 'able to become'. So a diagonalizable matrix is one that can be changed into a matrix with numbers only on that 'across' line, the diagonal, which makes calculations much simpler.