I found many information showed Schwarz inequality and Cauchy–Schwarz inequality are same on books and internet, but my teacher's material shows that:(adsbygoogle = window.adsbygoogle || []).push({});

Schwarz inequality:

[itex]\left\|[x,y]\right\|\leq\left\|x\right\|+\left\|y\right\|[/itex]

Cauchy–Schwarz inequality:

[itex]\left\|[x,y]\right\|\leq\left\|x\right\|\left\|y\right\|[/itex]

They seem to be different on material, and I had sent email to teacher but having no reply.

Therefore my question is "Are Schwarz inequality and Cauchy–Schwarz inequality same?"

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# Schwarz inequality is Cauchy–Schwarz inequality?

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