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"The main purpose of Linear algebra and linear models is to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution, and distributions of quadratic forms are developed along the way. For this third edition, the material has been reorganised to develop the linear algebra in the first six chapters. Other key features include, coverage of topics such as rank additivity, inequalities for eigenvalues and singular values, a new chapter on linear mixed models, over seventy additional problems on rank : the matrix rank is an important and rich topic with connections to many aspects of linear algebra such as generalized inverses, idempotent matrices and partitioned matrices."

"This textbook on linear algebra includes the key topics of the usual topics, such as complex vector spaces, complex inner products, the Spectral theorem for normal operators, dual spaces, the minimal polynomial, the Jordan canonical form, and the rational canonical form, are covered, along with a chapter on determinants at the end of the book. In addition, there is material throughout the text on linear differential equations and how it integrates with all of the important concepts in linear algebra.This book has several distinguishing features that set it apart from other linear algebra texts. For example, Gaussian elimination is used as the key tool in getting at eigenvalues, it takes an essentially determinant-free approach to linear algebra, and systems of linear differential equations are used as frequent motivation for the reader. "

"Tugas akhir ini bertujuan untuk mencari taksiran parameter pada Generalized Linear Mixed Model (GLMM). Parameter-parameter dalam GLMM merupakan parameter untuk melihat efek fixed dan efek random dari variabel-variabel prediktor terhadap variabel respon. Hal ini yang membedakan dengan Generalized Linear Regression Model (GLRM), yang hanya memperhatikan efek fixed. GLRM merupakan perluasan dari model regresi linier berganda dalam hal asumsi variansi errornya tidak konstan. Pada tugas akhir ini, metode yang digunakan untuk mencari taksiran parameter pada GLMM adalah metode Best Linear Unbiased Prediction (BLUP). Teori dasar yang dibutuhkan pada metode BLUP ini adalah metode Lagrange dan teorema invers matriks partisi. "