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1) Let V, W be F vector spaces. Recall that a skew-symmetric map is a function f: V × V → W such that f(V₁, V₂) = −ƒ (V2, V₁) (a) Prove that an alternating map is always skew-symmetric Prove that if char (F) + 2 then a skew-symmetric map is also alternating

1) Let V, W be F vector spaces. Recall that a skew-symmetric map is a function f: V × V → W such that f(V₁, V₂) = −ƒ (V2, V₁) (a) Prove that an alternating map is always skew-symmetric Prove that if char (F) + 2 then a skew-symmetric map is also alternating

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1) Let V, W be F vector spaces. Recall that a skew-symmetric map is a function f: V × V → W such that ƒ(V₁, V2) = −ƒ (V₂, V₁) (a) (b) Prove that an alternating map is always skew-symmetric Prove that if char(F) + 2 then a skew-symmetric map is also alternating
Transcribed Image Text:1) Let V, W be F vector spaces. Recall that a skew-symmetric map is a function f: V × V → W such that ƒ(V₁, V2) = −ƒ (V₂, V₁) (a) (b) Prove that an alternating map is always skew-symmetric Prove that if char(F) + 2 then a skew-symmetric map is also alternating
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