## Pictorial proof that combinations of 3 independent vectors fill a 3-dimensional space

If three vectors (, , ) are independent then they will fill at least three planes ( from and , from  and , et cetera) (proof). These three planes will meet at the origin. For any arbitrary plane goes through the origin in the space. The plane cannot be parallel to any of the three above […]

## Pictorial proof that combinations of two independent vectors fill a plane

Let’s take the intution like this: Imagine that from the intersectional point of  and , you draw an arbitrary vector . From the head of , we can always draw a vector such that it’s parallel to the line containing vector , the head of will touch the head of and the tail of will always […]

## Learning From Data – A Short Course: Exercise B.1

Page 2: This exercise introduces some fundamental properties of vectors and bases. (a) Are the following sets of vectors dependent or independent? You can solve the equation system (with is a matrix of the set of vectors in consideration: ). If the equation system has no solution (except zero vector) then the set of vectors […]

## [Book Note] Computer Vision: A Modern Approach (2nd Edition)

Page 458: I’m not sure if I interpret the statement right but here is my guess: One of the risk function in the example should look like this: . Page 459: The cost when an is refused to decide is: . The following arguments are applied for the Algorithm 15.1: If then we will rather to fail […]