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
- 7 years ago
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- 2
- Type
- Video
- Language
- English
- Content Type
- text/html; charset=utf-8
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
History
August 22nd, 2017 7 years ago
Submitted by Petra Taylor
