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Figure from:Notes on Elementary Linear Algebra

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The fact that H extends T follows from the definition of H, and the property that H preserves the inner product is easy to check:

Figure 1 The fact that H extends T follows from the definition of H, and the property that H preserves the inner product is easy to check:

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Theorem 6.3. Given a bilinear form g:V x V — K, the following are equivalent:
Theorem 6.3. Given a bilinear form g:V x V — K, the following are equivalent: