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Little Linear Algebra

Little Linear Algebra. Contents: Linear vector spaces Matrices Special Matrices Matrix & vector Norms. Definition of Matrix

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Little Linear Algebra

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  1. Little Linear Algebra • Contents: • Linear vector spaces • Matrices • Special Matrices • Matrix & vector Norms

  2. Definition of Matrix A matrix is a collection of numbers arranged into a fixed number of rows and columns. Usually the numbers are real numbers. In general, matrices can contain complex numbers but we won't see those here. Here is an example of a matrix with three rows and three columns: The top row is row 1The leftmost column is column 1. This matrix is a 3x3 matrix because it has three rows and three columns. In describing matrices, the format is: rows X columns Each number that makes up a matrix is called an element of the matrix. The elements in a matrix have specific locations.

  3. Transpose of a matrix For matrix A of the form: With 3 rows and 2 columns the transpose is rotate the matrix to change rows into columns and columns into rows In the form The superscript T denotes transpose, sometimes we use * instead of T

  4. Matrix addition

  5. Matrix multiplication Scalar multiplication Ex.

  6. EX. EX.

  7. Properties of Multiplication

  8. Special structure Matrices 1- identity matrix 2- Diagonal matrix

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