Manuals/calci/HERMITIAN

MATRIX("HERMITIAN",order)


  • is the order of the Hermitian matrix.

Description

  • This function gives the Hermitian matrix of order 3.
  • A Hermitian matrix is defined as the square matrix with complex entries which is equal to its own conjugate transpose.
  • i.e., the matrix A is Hermitian if and only if  , where   denotes the conjugate transpose, which is equivalent to the condition Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a_{ij}=a^_{ji}} .
  • A hermetian matrix is also called as self-adjoint matrix.
  • The following matrix is the example of 3x3 Hermitian matrix:

 .

  • The diagonal elements must be real, as they must be their own complex conjugate.
  • An integer or real matrix is Hermitian iff it is symmetric.
  • In calci, users can change the order and number of the Hermitian matrices.

Examples

  • 1.MATRIX("hermitian")
-62 -48 + 4i 49 + -40i
-48 + -4i -54 0 + 34i
49 + 40i 0 + -34i -33
  • 2.MATRIX("hermitian",5)
-90 -75 + 79i 56 + -17i 92 + -51i -13 + -21i
-75 + -79i -19 -77 + -19i 42 + 47i 83 + -95i
56 + 17i -77 + 19i -60 -25 + -26i 88 + -81i
92 + 51i 42 + -47i -25 + 26i -89 -70 + -92i
-13 + 21i 83 + 95i 88 + 81i -70 + 92i -7

See Also

References