Operations on positive definite matrices

Task number: 2729

Show that for positive definite matrices \(\mathbf A\) and \(\mathbf B\):

  • Variant 1

    The matrix \(\mathbf A+\mathbf B\) is also positive definite.

  • Variant 2

    The matrix \(\mathbf A^{-1}\) is also positive definite (i.e. show also that \(\mathbf A\) is regular).

Difficulty level: Moderate task
Proving or derivation task
Cs translation
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