Let V be a vector space, let B be a symmetric bilinear form onV, and let < . , .

ID: 2937632 • Letter: L

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Let V be a vector space, let B be a symmetric bilinear form onV, and let < . , .> be an inner product on V. What does itmean for a vector u in V to be an eigenvector of B with resepect to< . , .> with eigenvalue ? I know this relation: B(u, u) = <u, u>so that when the bilinear form acts on the vector u itproduces a scalar multiple of the inner product of u. But i'm notsure how to better explain that or whether or not it answers thequestion. Any help would be greatly appreciated! Let V be a vector space, let B be a symmetric bilinear form onV, and let < . , .> be an inner product on V. What does itmean for a vector u in V to be an eigenvector of B with resepect to< . , .> with eigenvalue ? I know this relation: B(u, u) = <u, u>so that when the bilinear form acts on the vector u itproduces a scalar multiple of the inner product of u. But i'm notsure how to better explain that or whether or not it answers thequestion. Any help would be greatly appreciated!

Explanation / Answer

the eigen values and the respective eigen vectors form thebasis to the given vector space. the bilinear form on a vector space is nothing but an innerproduct and consequently, the eigen vectors form the orthonormalbasis to the given inner product space .

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Let V be a vector space, let B be a symmetric bilinear form onV, and let < . , .

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