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📐 Mathematics  ·  Matrices  ·  JEE

Schur decomposition states that every square matrix A can be written as A = QTQ<sup>-1</sup> where:

Answer: T is upper triangular and Q is unitary.

  • A T is diagonal
  • B T is lower triangular and Q is orthogonal
  • C T is upper triangular and Q is unitary
  • D Q = I

Correct answer: C. T is upper triangular and Q is unitary

Explanation: Schur: every complex square matrix can be unitarily upper-triangularized: A = QTQ* where Q is unitary and T is upper triangular.

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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