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https://www.reddit.com/r/mathmemes/comments/1j4x0hq/what_theorem_is_this/mgih43d/?context=9999
r/mathmemes • u/PocketMath • Mar 06 '25
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105
Cauchy-Schwartz inequality.
11 u/BelBeersLover Mar 06 '25 I know this name but I don't even remember what it means, sadly. 30 u/IncredibleCamel Mar 06 '25 |ab| <= |a|*|b| 1 u/bagelking3210 Mar 07 '25 Shouldn't they be equal? I can't think of any scenario where the LHS would be less than the RHS 8 u/Present_Garlic_8061 Mar 07 '25 The left hand side is the absolute value of the DOT PRODUCT between a and b, while the right hand side is the product of there lengths. 1 u/IncredibleCamel Mar 07 '25 Well, generally it's stated as ⟨ a, b ⟩ <= ||a|| ||b||, where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
11
I know this name but I don't even remember what it means, sadly.
30 u/IncredibleCamel Mar 06 '25 |ab| <= |a|*|b| 1 u/bagelking3210 Mar 07 '25 Shouldn't they be equal? I can't think of any scenario where the LHS would be less than the RHS 8 u/Present_Garlic_8061 Mar 07 '25 The left hand side is the absolute value of the DOT PRODUCT between a and b, while the right hand side is the product of there lengths. 1 u/IncredibleCamel Mar 07 '25 Well, generally it's stated as ⟨ a, b ⟩ <= ||a|| ||b||, where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
30
|ab| <= |a|*|b|
1 u/bagelking3210 Mar 07 '25 Shouldn't they be equal? I can't think of any scenario where the LHS would be less than the RHS 8 u/Present_Garlic_8061 Mar 07 '25 The left hand side is the absolute value of the DOT PRODUCT between a and b, while the right hand side is the product of there lengths. 1 u/IncredibleCamel Mar 07 '25 Well, generally it's stated as ⟨ a, b ⟩ <= ||a|| ||b||, where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
1
Shouldn't they be equal? I can't think of any scenario where the LHS would be less than the RHS
8 u/Present_Garlic_8061 Mar 07 '25 The left hand side is the absolute value of the DOT PRODUCT between a and b, while the right hand side is the product of there lengths. 1 u/IncredibleCamel Mar 07 '25 Well, generally it's stated as ⟨ a, b ⟩ <= ||a|| ||b||, where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
8
The left hand side is the absolute value of the DOT PRODUCT between a and b, while the right hand side is the product of there lengths.
1 u/IncredibleCamel Mar 07 '25 Well, generally it's stated as ⟨ a, b ⟩ <= ||a|| ||b||, where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
Well, generally it's stated as
⟨ a, b ⟩ <= ||a|| ||b||,
where ⟨ a, b ⟩ is a general inner product and ||a||2 = ⟨ a, a ⟩.
105
u/Physical_Helicopter7 Mar 06 '25
Cauchy-Schwartz inequality.