Systems of linear equations; Gaussian elimination. Vector spaces, subspaces, linear, independence, dimension, change of basic. Linear transformations. Inner product, orthogonality. Eigenvalues. Diagonalization and canonical forms. Cayley-Hamilton theorem.

### Linear Algebra (MATH 201)

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Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | |||

BA-Economics | |||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Electronics Engineering | * | ||

BS-Electronics Engineering | * | ||

BS-Industrial Engineering | * | ||

BS-Manufacturing Systems Eng. | * | ||

BS-Materials Sci. & Nano Eng. | * | ||

BS-Materials Science & Eng. | * | ||

BS-Mechatronics | * | ||

BS-Mechatronics | * | ||

BS-Microelectronics | * | ||

BS-Molecular Bio.Gen.&Bioeng | * | ||

BS-Telecommunications | * | ||

Mathematics | * |

### CONTENT

### OBJECTIVE

This course aims to introduce basic concepts of linear algebra such as vector spaces, bases, linear transformations, eigenvalues and eigenspaces. The course gives students training to develop their mathematical skills, analytical and critical thinking abilities, their ability to apply these capabilities to practical problems, and to communicate their knowledge of these areas.

### LEARNING OUTCOME

Understand the notion of mathematical thinking, mathematical proofs, and able to apply them in problem solving.

Present simple proofs in a precise and formally correct way.

Solve a system of linear equations using matrix reduction

Do basic arithmetical operations with matrices.

Understand the notions of linear independence, basis and dimension of a vector space.

Find a basis and dimension of Euclidean or abstract vector spaces.

Geometrically interpret the above concepts.

Represent linear transformations as matrices and, conversely, interpret matrices as linear maps.

Compute determinant of square matrices and understand the properties of determinant.

Compute eigenvalues and eigenspaces of matrices.

Identify whether a matrix is diagonalizable or not.

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 35 |

Midterm | 60 |

Participation | 5 |

### RECOMENDED or REQUIRED READINGS

Readings |
Strang, G., Introduction to Linear Algebra, 5th edition, Wellesley-Cambridge Press and SIAM, 2016. (Majority of homework problems will be assigned from this book.) |