Inner product of two vectors in R^n, length of a vector in R^n, orthogonality. Motivation via approximate solutions of systems of linear equations, definition and properties of inner product (symmetric, bilinar, positive definite); length/norm of a vector, unit vectors; definition of distance between vectors; definition of orthogonality; Pythagorean Theorem.

- Created On
- August 22nd, 2017
- 5 years ago
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- English
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##### Definition of inner product, real entries, coordinate setting math.la.d.innerproduct.real.coord

##### The standard inner product is commutative, coordinate setting. math.la.t.innerproduct.commutative.coord

##### The standard inner product distributes over addition, coordinate setting. math.la.t.innerproduct.distributive.coord

##### The standard inner product of a vector with itself is zero only for the zero vector, coordinate setting. math.la.t.innerproduct.self.z.coord

##### Definition of norm/length of a vector, coordinate setting math.la.d.vec.norm.coord

##### Definition of unit vector, coordinate setting math.la.d.vec.unit.coord

##### Definition of distance, coordinate setting math.la.d.distance.coord

##### Definition of two vectors being orthogonal math.la.d.vec.orthogonal

##### Two vectors are orthogonal if and only if the Pythagorean Theorem holds. math.la.t.vec.orthogonal