Question

Let

A = \begin{bmatrix} 2 & 2 & 1\\ -1 & -1 & 2\\ 0 & 0 & -2 \end{bmatrix}

Find a unitary matrix U such that U^*AU is upper triangular.

06 Feb 2024
Answer :
Word Count : 441

To find a unitary matrix \( U \) such that \( U^*AU \) is upper triangular, we can use the Schur decomposition theorem. According to this theorem, any square matrix \( A \) can be decomposed as \( A = QUQ^* \), where \( Q \) is unitary and \( U \) is upper triangular.

Given matrix \( A \):

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