Let x1,x2,x3,x4,x5 be a system of orthonormal vectors in \(\mathbb{R}^{10}\).…

GATE · 2025 · DA · Data Science & AI

Let x1,x2,x3,x4,x5 be a system of orthonormal vectors in R10\mathbb{R}^{10}. Consider the matrix A=x1x1⊤+…+x5x5⊤A=x_1x_1^\top+\ldots+x_5x_5^\top. Which of the following statements is/are correct?

  1. A.

    Singular values of A are also its eigenvalues

  2. B.

    Singular values of A are either 0 or 1

  3. C.

    Determinant of A is 1

  4. D.

    A is invertible

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