21 The triangle inequality says: (length of v + w) ≤ (length of v) + (length of w). Problem 19 found ||v + w||² = ||v||² +2v • w+ ||w||². Use the Schwarz inequality v • w ≤ ||v|| ||w|| to show that || side 3|| can not exceed ||side 1|| + ||side 2||: ||v + w|| ² ≤ (||v|| + ||w||) ² or ||v+w|≤||v|| + ||w||. Triangle inequality

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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21
The triangle inequality says: (length of v+w) ≤ (length of v) + (length of w).
Problem 19 found ||v + w||² = ||v||² + 2v • w + ||w||². Use the Schwarz inequality
v • w ≤ ||v|| ||w|| to show that ||side 3|| can not exceed || side 1|| + ||side 2||:
|| v + w||² ≤ (||v|| + ||w||) ² or ||v + w || ≤ || v || + ||w||.
Triangle
inequality
Transcribed Image Text:21 The triangle inequality says: (length of v+w) ≤ (length of v) + (length of w). Problem 19 found ||v + w||² = ||v||² + 2v • w + ||w||². Use the Schwarz inequality v • w ≤ ||v|| ||w|| to show that ||side 3|| can not exceed || side 1|| + ||side 2||: || v + w||² ≤ (||v|| + ||w||) ² or ||v + w || ≤ || v || + ||w||. Triangle inequality
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