Linear Alg: Projection is closest vector in subspace
Loading...
Loading...
5,575
Loading...
There is no Interactive Transcript.
14:37
Introduction to Projectionsby khanacademy23,603 views- 15:32
Linear Algebra: Least Squares Approximationby khanacademy25,573 views
- 16:40
Expressing a Projection on to a line as a Matrix Vector prodby khanacademy13,674 views
- 13:04
Linear Algebra: Subspace Projection Matrix Exampleby khanacademy12,355 views
- 48:51
Lec 15 | MIT 18.06 Linear Algebra, Spring 2005by MIT39,630 views
- 19:00
Linear Algebra: Basis of a Subspaceby khanacademy105,513 views
- 25:33
Linear Algebra: Vector Examplesby khanacademy80,455 views
- 10:23
Introduction to the Null Space of a Matrixby khanacademy54,012 views
- 13:07
Null Space 2: Calculating the null space of a matrixby khanacademy53,633 views
- 25:11
Defining the angle between vectorsby khanacademy31,612 views
- 17:32
Linear Transformations as Matrix Vector Productsby khanacademy41,822 views
- 12:12
Point distance to planeby khanacademy11,402 views
- 16:31
Linear Algebra: Introduction to Vectorsby khanacademy136,295 views
- 19:14
Dot and Cross Product Comparison/Intuitionby khanacademy22,323 views
- 13:52
Linear Transformationsby khanacademy82,313 views
- 9:48
Housing Price Conundrum (part 3)by khanacademy86,602 views
- 6:59
Unit Vectorsby khanacademy27,007 views
- 9:10
Vector Dot Product and Vector Lengthby khanacademy51,460 views
- 13:14
Linear Algebra: Gram-Schmidt Process Exampleby khanacademy24,070 views
@tadm123
Establishing uniqueness is actually a big deal in math. He'd done all the setup work to establish it (it was just a brief comment away), but forgot to make that final observation. Yeah - no need to unsubscribe - he does good stuff, including this vid.
VeryEvilPettingZoo 9 months ago
@VeryEvilPettingZoo he missed a "the"? wtf *unsubscribed*
Sarcasm obviously.
tadm123 9 months ago
You've proven that every vector in the subspace is at least as far from x as its projection (denoted Proj(V, x)). You could complete this insight by using that your inequality is strict ("less than", instead of "less than or equal to") whenever the length of b is not 0, hence whenever b is not 0. But b = 0 only if v = Proj(V, x). Thus any vector in the subspace OTHER than Proj(V, x) is FARTHER from x than Proj(V, x). Thus the projection vector is THE closest vector in the subspace.
VeryEvilPettingZoo 2 years ago