Linear Algebra Lecture 2.

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Presentation transcript:

Linear Algebra Lecture 2

Introduction to Matrices

Matrix

Matrix

Definitions Square Matrix Equality of Matrices Column Matrix Row Matrix (Vector) Multiple of a Matrix

Example 1

Algebra Addition of Matrices Subtraction of Matrices Multiplication of Matrices

Example 2

Multiplication

Multiplicative Identity

Zero Matrix

Commutative Law A+B = B+A AB=BA ? (NO)

Associative Law A+(B+C) = (A+B)+C A(BC)=(AB)C

Distributive Law A(B+C) = AB + AC (A+B)C = AC + BC

Determinant of a Matrix

Example

Definitions Transpose of a Matrix Symmetric Matrix Singular Matrix Non-Singular Matrix

Multiplicative Inverse

Matrix Calculus Derivative of a Matrix of Functions Integral of a Matrix of Functions

Linear Algebra Lecture 2