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Glite Dictionary
characteristic root

characteristic root

9.9
A number that makes a square matrix have determinant zero when subtracted from its diagonal entries
  • noun
  • Specialized
translation icon : raíz característica
  • The characteristic roots of the matrix determine its stability in dynamic systems.

Examples

  • To find a characteristic root, solve the matrix's characteristic equation.

  • Every square matrix has at least one characteristic root.

  • The characteristic root is crucial.

  • What is a characteristic root?

  • Every square matrix has at least one characteristic root.

  • The characteristic roots of a matrix can be found using its characteristic equation.

  • Calculating the characteristic root helps in understanding the behavior of the matrix.

Synonyms

eigenvalue
vscharacteristic root
  • Specialized
2 9.9

A number for a square matrix that makes some nonzero vector bigger or smaller when multiplied by the matrix

is the identical concept expressed with an alternative name

Surface Forms

characteristic root singular
characteristic roots plural

Morphology

characteristic + root

The constituents 'characteristic' (a property) and 'root' (a solution) provide a partial cue that this is a kind of solution associated with a characteristic equation of a matrix. However, the precise technical meaning (an eigenvalue) is specialised mathematical knowledge and not fully derivable by a B1 learner who only knows the ordinary senses of the component words.

Etymology

Characteristic root combines two images: characteristic means an important feature of a matrix, and root means a number that makes a special equation zero. So a characteristic root is the number, also called an 'eigenvalue', that reveals an important property of the matrix.