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Glite Dictionary
to diagonalize

to diagonalize

1 9.9
To change a matrix so only the main diagonal has numbers that are not zero
  • verb
  • /daɪˈæɡənəˌlaɪz/
  • Specialized
: diagonalizar
  • In linear algebra, one often learns how to diagonalize matrices for simplifying calculations.

Is there any physical interpretation to diagonalizing that matrix?

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Examples

  • So that process is called diagonalizing the weight matrix, OK.

  • Is there any physical interpretation to diagonalizing that matrix?

    MIT OpenCourseWare

  • Now the key is to try to diagonalize this as much as possible such that the win, win and lose lose.

    Tim Ferriss

  • So all predictions and all observed experimental results are equivalent to assuming that this particular ? is the density matrix of the system, but if we diagonalize ? we see that its true ontic basis is something else entirely.

    Blog text (29)

  • At every instant of time, the density matrix is always a Hermitian, positive-definite, trace-one matrix, so you can always diagonalize it, and its eigenvalues are always real, positive, and sum to one.

    Blog text (29)

  • To analyze the system's dynamics, we need to diagonalize the matrix representing its equations.

  • When we diagonalize the given matrix, it reveals the principal axes of the transformation.

Surface Forms

diagonalize infinitive
diagonalized past
diagonalized past participle
diagonalizing present participle
diagonalizes third person singular

Morphology

diagonalize = diagonal (transparent) = diagonal + ize

Formed by the productive verb-forming suffix '-ize' added to the English adjective 'diagonal', meaning 'to make or become diagonal' which matches the mathematical usage.

Etymology

Diagonalize comes from diagonal, which originally meant 'from corner to corner' or 'from angle to angle'. So to diagonalize a matrix is to change it so that only the numbers on the main 'corner-to-corner' line remain, and that makes many calculations much easier.