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

Infuriate

Triangulation from Three Views,nts in the presence of noise, in such a way that their rays, or their lines of sight, intersect at a single point in the scene. We show that three rays intersect in the scene if and only if the “trilinear constraint,” specified by the “trifocal tensor,” is satisfied. We discuss its geometric meaning

夜晚

Pseudoinverse,ses. We point out that we need a special care for computing the pseudoinverse of a matrix whose elements are obtained by measurement in the presence of noise. We also point out that the error in such matrices is evaluated in the “matrix norm.”

Neutropenia

Fitting Spaces,m the spectral decomposition of a matrix, which we call the “covariance matrix,” but also can be obtained from its singular value decomposition. We point out that the use of the singular value decomposition is more efficient with smaller computational complexity.

amputation

LAIR

斗志

Linear Space and Projection, the projection matrix. As an illustration, we show examples of projection onto lines and planes and introduce the “Schmidt orthogonalization” for producing an orthonormal system of vectors using projection matrices.

IDEAS

看法等

Least-Squares Solution of Linear Equations, 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 solution is obtained without using differentiation or normal equations. As illustrative examples, we show the case of multiple equations of one variable and the case of a single multivariate equation.

Mangle

Triangulation from Three Views,s intersect in the scene if and only if the “trilinear constraint,” specified by the “trifocal tensor,” is satisfied. We discuss its geometric meaning and point out the role of pseudoinverse in the course of iterative optimal computation.

Abduct