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Linear algebra

Course Description: A general review of vectors in n-dimensional Euclidean space, and linear transformations from n-dimensional space to m-dimensional space and their properties. General vectors in space, subspaces, linear independence, row space, column space, and null space. Inner product in space, angle and orthogonality in inner product spaces, best approximation: least squares, and orthogonal matrices. Eigenvalues and eigenvectors.
Credit hours: 3
Prerequisites: MATH107
Objectives of the course :

The goal of this module is to:
(A) Understanding the concept of n-dimensional Euclidean space, and linear transformations from m-dimensional Euclidean space to n-dimensional Euclidean space.

(B) Description and distinction of general vector space, subspace, linear independence, and linear dependence.

(c) Familiarity with the row space, column space, and null space.

(d) Understanding the inner product in space, and angle and orthogonality in inner product space.

(e) Better approximation understanding; the least squares method.

Course outputs :

1. Acquiring the concept of n-dimensional Euclidean space and the linear transformation from m-dimensional Euclidean space to n-dimensional Euclidean space.

2. Definition of a general vector space, subspace, linear independence, and linear dependence.

3. Description of inner product spaces, orthogonal matrices, and diagonalizable matrices.

4. Finding the best approximation using the least squares method.

5. Acquiring the fundamental concepts and properties of vectors in two-dimensional, three-dimensional, and n-dimensional spaces.

6. Calculating the row space, column space, and null space.

7. Calculation of eigenvalues and eigenvectors for matrices.

8. Discussion of Angle and Orthogonality in Inner Product Spaces.

9. Calculation of least squares solutions for a system of linear equations.

Additional information:
  • Last updated: 2026-05-17

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