LA9

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Show that the zero matrix \mathcal{O}\, is self-adjoint.

\langle \mathcal{O}x, y\rangle = \langle \vec{0}, y\rangle
= 0\,

and

\langle x, \mathcal{O}y\rangle = \langle x, \vec{0}\rangle
= 0\,

Thus, \langle \mathcal{O}x, y\rangle = \langle x, \mathcal{O}y\rangle. Therefore, \mathcal{O}\, is the adjoint of \mathcal{O}\,, or, in other words, \mathcal{O}\, is self-adjoint.


Main Page : Linear Algebra

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