About the book
Projective geometry has a long history of development, which can be traced back to the 4th century BC when the ancient Greeks discovered the conic curve. Until the 17th century, the French mathematician R. Descartes (1596-1650) algebraized geometry, i.e. solved geometric problems by using algebraic equations, which led to the emergence of analytic geometry, followed by analytic projective geometry. Projective geometry mainly studies the invariant geometric properties of graphics under projective transformation. It has beautiful mathematical principles and contents such as duality principle, continuity principle, and butterfly theorem. "all geometry is projective geometry!" said by British mathematician A. Cayley (1821-1895). With the development of algebraic theory and the application of the determinant theory of equations and coordinate transformation methods, projective geometry has been applied and developed in various fields, especially in large data analysis, such as principal component analysis, independent component analysis, pattern classification, and recognition, etc. This book focuses on the application of projective geometry in principal component analysis, independent component analysis, and pattern classification and recognition.