Linear Algebra Volume 02 Matrix Representation, Kernel, Image, and Orthogonality (Graduate Mathematics Book 5)

Linear Algebra Volume 02: Matrix Representation, Kernel, Image, and Orthogonality (Graduate Mathematics Book 5)
English | April 28, 2026 | ASIN: B0GX2Z49HW | 541 pages | PDF | 12.62 MB
Linear Algebra Volume 02Matrix Representation, Kernel, Image, and OrthogonalityThis book is the second volume in the Linear Algebra series, designed for advanced students, teachers, and professionals who wish to deepen their understanding of linear transformations and their matrix representation.The text develops essential topics such as the kernel and image of linear transformations, matrix representation, rank, Gaussian elimination, LU factorization, inner products, orthogonality, the Gram-Schmidt process, QR factorization, adjoint transformations, and the Fundamental Theorem of Linear Algebra.With clear definitions, rigorous theorems, detailed proofs, solved examples, and proposed exercises, this volume connects algebraic theory with geometric intuition and practical applications in engineering, physics, statistics, economics, and applied sciences.Inside this book, you will find:Kernel, image, and projectionsMatrix representation of linear transformationsMatrix rank and elimination methodsLU decomposition and systems of linear equationsInner products and orthogonalizationGram-Schmidt process and QR factorizationAdjoints and the four fundamental spacesThis volume is ideal for readers who already know the foundations of vector spaces and linear transformations and want to advance toward a deeper and more structured understanding of modern linear algebra.