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📐 Mathematics  ·  Matrices  ·  JEE

For a Hermitian matrix H, the defining property is:

Answer: H = H dagger (conjugate transpose).

  • A H = H<sup>T</sup>
  • B H = -H (conjugate transpose)
  • C H = H* (conjugate)
  • D H = H<sup>dagger</sup> (conjugate transpose)

Correct answer: D. H = H<sup>dagger</sup> (conjugate transpose)

Explanation: A Hermitian matrix satisfies H = H<sup>dagger</sup> (H equals its own conjugate transpose). Eigenvalues of a Hermitian matrix are always real.

Matrix A (3 rows x 3 columns)a11a12a13a21a22a23a31a32a33column 1column 2column 3row 1row 2row 3

Element aij of matrix A sits at the intersection of row i and column j.

Concept context

Matrix operations, determinants, inverses, and solving linear systems

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