EKMZ203 Linear Algebra

Information

Course Goal / Objective

Be able to perform matrix operations and solve linear equation systems. It is aimed that they understand vector spaces and grasp fundamental concepts such as linear independence, basis, and dimension. Through these topics, students are expected to apply their theoretical knowledge to practical problems and develop their analytical thinking skills.

Course Content

The course content covers matrices and matrix operations, including special types of matrices, elementary row and column operations, echelon form, and the rank of a matrix. Elementary matrices, inverse matrices, and determinants are examined in detail, focusing on determinant properties, signed minors, and the adjugate matrix. Equivalent matrices and methods for obtaining inverse matrices are discussed, along with solutions to linear equation systems using Cramer's rule and the Gaussian elimination method. Vector spaces and subspaces are explored, covering linear independence, basis and dimension, coordinates, and basis transformation. Inner product spaces, the standard inner product function, and orthogonal bases are introduced, with an emphasis on the Gram-Schmidt process, orthogonal subspaces, and the orthogonal complement of a subspace. Linear transformations are analyzed, including the kernel and rank of a linear transformation, as well as their representation using matrices. Eigenvalues and eigenvectors are studied, along with diagonalization, the Cayley-Hamilton theorem, and quadratic forms. Finally, Hermitian forms and various numerical applications are examined.

Course Precondition

no prerequisites

Resources

Kolman, B., Hill, D. R., & Akın, Ö. (2002). Uygulamalı lineer cebir. Palme Yayıncılık.

Notes

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Course Learning Outcomes

Relation with Program Learning Outcome

Week Plan

Student Workload - ECTS