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(a) Prove that the set of all (M) tensors for fixed M, N forms a vector space. (You must define addition of such tensors and their multiplication by numbers.) (b) Prove that a basis for this space is the set {ea Dēß. Dey & w¹ ã' ... wª). ! © M vectors N one-forms (You will have to define the outer product of more than two one-forms.)

(a) Prove that the set of all (M) tensors for fixed M, N forms a vector space. (You must define addition of such tensors and their multiplication by numbers.) (b) Prove that a basis for this space is the set {ea Dēß. Dey & w¹ ã' ... wª). ! © M vectors N one-forms (You will have to define the outer product of more than two one-forms.)

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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23 (a) Prove that the set of all (M) tensors for fixed M, N forms a vector space. (You must define addition of such tensors and their multiplication by numbers.) (b) Prove that a basis for this space is the set {ea eß ... Dey & will M vectors N one-forms (You will have to define the outer product of more than two one-forms.) ' ... '¹}.
Transcribed Image Text:23 (a) Prove that the set of all (M) tensors for fixed M, N forms a vector space. (You must define addition of such tensors and their multiplication by numbers.) (b) Prove that a basis for this space is the set {ea eß ... Dey & will M vectors N one-forms (You will have to define the outer product of more than two one-forms.) ' ... '¹}.
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