The Cauchy-Schwarz inequality says a dot product can never exceed the product of the lengths. |u · v| ≤ ‖u‖ ‖v‖ Equality holds exactly when the two vectors are parallel. It follows from u · v = ‖u‖ ‖v‖ cos θ, since |cos θ| is at most 1. The same statement reappears for vectors, for integrals as (∫fg)² ≤ (∫f²)(∫g²), and for probability as (E[XY])² ≤ E[X²]E[Y²]. The correlation coefficient lies between minus 1 and 1 for exactly this reason.
In this video I show that the absolute value of the dot product has a maximum value of the lengths of each vector multiplied by each other. This relation is known as the Cauchy-Schwarz Inequality.
Prove Cauchy Schwarz Inequality
Cauchy-Schwarz Inequality - MATHEMATICS & NATURE
In sociology, we often try to isolate variables like race or class, but Newman argues that these identities are inseparable and mutually reinforcing. You cannot understand someone's experience of gender without also considering their economic status and sexual orientation. This 'matrix of domination' means that a person can simultaneously hold positions of privilege and subordination depending on the context. Instead of looking at inequalities as separate issues, we must see them as a complex we
State And Prove Cauchy Schwarz Inequality
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Equality and equity - Sketchplanations
Cauchy Schwarz Inequality Vectors
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