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For two n-dimensional vectors [tex]\mathbf{v}_1\text{ and }\mathbf{v}_2[/tex], what is the Cauchy-Schwarz Inequality:

1- [tex]|\mathbf{v}_1.\mathbf{v}_2|\leq\|\mathbf{v}_1\|\|\mathbf{v}_2\|[/tex], or

2- [tex]|\mathbf{v}_1.\mathbf{v}_2|\leq\|\mathbf{v}_1\|+\|\mathbf{v}_2\|[/tex]

In either case, the equality holds when [tex]\mathbf{v}_1=a\,\mathbf{v}_2[/tex], where a is a positive real constant. Is there any specific way to compute a, or just pick an arbitrary positive real number?

Regards

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# Cauchy-Schwarz Inequality

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