Printout of the Proofs of Theorems in Section 2.1. Basic Vector/Matrix Structure and Notation. Solutions and Hints for Selcted Exercises.Ĭhapter 1. Special Matrices and Operations Useful in Modeling. Evaluation of Eigenvalues and Eigenvectors. Matrix Transformations and Factorizations.
#MATRICES PDF NOTES PDF#
The "Printout of Proofs" are printable PDF files of the Beamer slides without the pauses. The "Proofs of Theorems" files were prepared in Beamer and they contain proofs of results which are particularly lengthy (shorter proofs are contained in the notes themselves). A more abstract approach to linear algebra can be found in the online notes for Linear Algebra (Graduate Level), based on Thomas Hungerford's Algebra (Springer-Verlag, 1974).Ĭopies of the classnotes are on the internet in PDF format as given below. For example, we will deal with matrices with real entries and not deal with the entries as elements of a field nor with the more abstract algebra properties of matrices. We will not take as much of a theoretical approach as I do in my other graduate-level classes. Results contained in Gentle's book are numbered as (such as "Theorem 3.2.1") and labeled results from other sources are numbered by the chapter, section, and a letter (such as "Theorem 3.2.A"). No 'Proof' and 'Q.E.D.' or '■' appear to indicate beginning and end." We will follow a different approach and will be introducing exactly the definition/theorem/proof approach in these class notes. Most of the facts have simple proofs, and most proofs are given naturally in the text. The author of the text states (see page viii) ".the presentation is informal neither definitions nor facts are highlighted by words as 'Definition', 'Theorem', 'Lemma', and so forth. The class covers the first 5 chapters of the textbook, Matrix Algebra: Theory, Computations, and Applications in Statistics, which is the "Theory" part of the book (Chapters 6 and 7 are in the "Linear Algebra" part of the book, but actually address more computational material). This is why we use a textbook in the "Springer Texts in Statistics" series. The catalog description of Theorey of Matrices (MATH 5090) is very brief: "Vector spaces, linear transformations, matrices, and inner product spaces." In light of our department's name, "The Department of Mathematics and Statistics," this class will try to branch these two areas. They also provide insights into many mathematical areas.Matrix Algebra: Theory, Computations, and Applications in Statistics, by James E. However, there is multiplication by the inverse.Įigenvalues and eigenvectors are used to understand how buildings, structures and automobiles react in real life. There is no division operation in matrix algebra. Systems of linear equations can have infinitely many solutions, no solution, or a unique solution. This is sometimes called Gaussian elimination. Systems of linear equations may be solved using elementary row operations. The determinant of a matrix can only be calculated for a square matrix and is used in many aspects of mathematics/engineering/physics. To multiply two matrices A and B, the number of columns in A must equal the number of rows in B. Matrices of the same shape (same number of rows and columns) may be added/subtracted by adding/subtracting the corresponding elements. M2 Addition and subtraction of matrices.This module discusses matrices, their order, row and column matrices, square matrices and the identity matrix. Improve your skills in the area of Matrices.Ī matrix is an array of numbers.