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LINEAR TRANSFORMATIONS, KERNELS AND IMAGES. INNER PRODUCTS, INNER PRODUCT SPACES, ORTHONORMAL SETS, GRAM-SCHMIDT PROCESS. EIGENVECTORS AND EIGENVALUES, DIAGONALIZATION, APPLICATIONS. SYMMETRIC AND HERMITIAN MATRICES. QUADRATIC FORMS, BILINEAR FORMS. JORDAN NORMAL FORM AND OTHER CANONICAL FORMS.
Linear Algebra II requires a good knowledge of basis and dimension before moving on to other parts of the course. Unlike Linear Algebra I where the main focus is on solving linear equations, Linear Algebra II is more on understanding transformations and knowing the different definitions and properties. My cohort is considered lucky, as our syllabus is limited to real vector spaces, thus there is no mentioning about complex and rational numerical operators. However, if one has good understanding of the topic in real spaces, then there will be somewhat partial understanding when dealing with other fields. :)
The course is generally difficult and abstract, and it takes a lot of time to understand the content of the course. Definitions are very important, and so is working with the given examples. It is super not advisable to skip any content in front and move on to the next topic, it doesn't help at all. So, if you don't understand anything in front, go understand first before moving on.
The midterm and finals are rushed papers. The midterm is rather easy though, definitions alone can give as easily about 65% of the marks. The finals is also much simpler than the previous year papers, since there is the absence of orthogonal complements, rational and complex operators. The difficult questions do not contain a lot of marks, an knowing just chapter one and two is enough for a person to score 50% of the finals paper. Studying and understanding really helps.
Despite the midterms being simple, the average score is 14/25. Maybe that's the nature of this course. Anyway my lecturer is excellent! Dr Le.Ha Khoi? If the lecturer is him, don't skip his lectures, he explains things very clearly! It's not difficult to see that the cohort has improved because of his teaching. :) Not recommended as UE to any non-maths student, the abstract is too concept and has a lot of content.