Titlebook: Linear Algebra for Pattern Processing; Projection, Singular Kenichi Kanatani Book 2021 Springer Nature Switzerland AG 2021

Absenteeism

affinity

盟军

制造

Sedative

Singular Values and Singular Value Decomposition,xtend it to arbitrary rectangular matrices; we define the “singular value decomposition,” which expresses any matrix in terms of its “singular values” and “singular vectors.” The singular vectors form a basis of the subspace spanned by the columns or the rows, defining a projection matrix onto it.

coagulate

Pseudoinverse,lar matrix. While the usual inverse is defined in such a way that its product with the original matrix equals the identity, the product of the pseudoinverse with the original matrix is not the identity but the projection matrix onto the space spanned by its columns and rows. Since all the columns an

sacrum

Least-Squares Solution of Linear Equations,doinverse has been studied in relation to minimization of the sum of squares of linear equations. The least-squares method usually requires solving an equation, called the “normal equation,” obtained by letting the derivative of the sum of squares be zero. In this chapter, we show how a general solu

英寸

使迷惑

Fitting Spaces, a given set of points in .D. A subspace is a space spanned by vectors starting from the origin, and an “affine space” is a translation of a subspace to a general position. The fitting is done hierarchically: we first fit a lower dimensional space, starting from a 0D space (= a point), then determin

BLA

Matrix Factorization,A .. We discuss its relationship to the matrix rank and the singular value decomposition. As a typical application, we describe a technique, called the “factorization method,” for reconstructing the 3D structure of the scene from images captured by multiple cameras.