1. Linear Algebra 1.Basic concepts 2.Matrix operations

2. Basic Concepts l m-dimensional column vector l n-dimensional row vector l mxn-dimensional matrix l Square matrix: m = n

3. Matrix Addition & Subtraction l Only possible for matrices of same dimension l Add/subtract matrices element-by-element l Addition example: C = A+B l Subtraction example: C = A-B

4. Scalar and Matrix Multiplication l Scalar multiplication »B = kA »Dimensions: »General formula: »Example l Matrix multiplication »C = AB »Only possible if the number of columns of A is equal to the number of rows of B

5. Matrix Multiplication cont. l General representation »Dimensions: »Formula l Examples l Noncommutative operation:

6. Transpose l Notation: B = A T l Dimensions: l Formula: l Example l Important properties

7. Common Matrices l Symmetric matrix: A T = A l Skew-symmetric matrix: A T = -A l Example of a diagonal matrix l Examples of triangular matrices l Identity matrix

8. Systems of Linear Algebraic Equations l Scalar representation l Matrix representation: Ax = b l Homogeneous system: b = 0 »One obvious solution: x = 0

9. Triangular Systems l Example l Solution l Gaussian elimination »Transform original system into diagonal form »Accomplished by elementary row operations

10. Systems of Linear Algebraic Equations l Scalar representation l Matrix representation: Ax = b l Homogeneous system: b = 0 »One obvious solution: x = 0