The Vector Triangle Inequality is directly from the Cauchy-Schwarz Inequality. The vector-triangle inequality is to test for linear dependence of linear independence. We can relate this to the inequalities learned in introductory geometry.
When labeling the sides of a triangle, use a, b, and c. A point on a triangle is a vertex and is the fastest way to get from one point to another. If two points are co-linear, then the route between them is the same as the route between the points themselves.
When you have an acute or right triangle then the triangle inequality will hold. You will want to translate the triangle inequality to the vector triangle inequality.
Two vectors share an origin, and are sides of a triangle with three sides. The length of a vector helps to understand how large the vector is in terms of dimensions. When adding vectors, take one vector, and fix the initial point to the terminal point of the other vector.
When the sum of the vectors is less than the sum of the lengths of the vectors, the two vectors of this problem are linearly independent.
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This video tutorial works through math problems/equations that address topics in Linear Algebra. This specific tutorial addresses Vector triangle inequality.
Length: 11 minutes
Copyright date: ©2019
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