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For Lie algebras of type Bn: There is a correspondence between matrices and bilinear forms given by B(v, w) v' Aw. (i) Find necessary and sufficient conditions on A so that the corresponding bilinear form B is symmetric i.e. B(v, w) = B(w, v).

For Lie algebras of type Bn: There is a correspondence between matrices and bilinear forms given by B(v, w) v' Aw. (i) Find necessary and sufficient conditions on A so that the corresponding bilinear form B is symmetric i.e. B(v, w) = B(w, v).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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For Lie algebras of type Bn: There is a correspondence between matrices and bilinear forms given by B(v, w) = v' Aw. (i) Find necessary and sufficient conditions on A so that the corresponding bilinear form B is symmetric i.e. B(v, w) = B(w, v).
Transcribed Image Text:For Lie algebras of type Bn: There is a correspondence between matrices and bilinear forms given by B(v, w) = v' Aw. (i) Find necessary and sufficient conditions on A so that the corresponding bilinear form B is symmetric i.e. B(v, w) = B(w, v).
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