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Exercise 6.8.2

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The property 1 comes from the definition of a bilinear form. The property 2 comes from that $L_{x} (0) = R_{x} (0) = 0$ . The property 3 comes from the computation

H (x + y, z + w) = H (x, z + w) + H (y, z + w)

= H (x, z) + H (x, w) + H (y, z) + H (y, w) .

Finally, the condition in the definition of a bilinear form is symmetric for the first and the second component. Thus, we get the property 4.

jephianlin

2011-06-27 00:00

Exercise 6.8.2

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