matrix operations. matrix notation example equality of matrices

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Matrix Operations

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Page 1: Matrix Operations. Matrix Notation Example Equality of Matrices

Matrix Operations

Page 2: Matrix Operations. Matrix Notation Example Equality of Matrices

Matrix Notation

Page 3: Matrix Operations. Matrix Notation Example Equality of Matrices

Example

Page 4: Matrix Operations. Matrix Notation Example Equality of Matrices

Equality of Matrices

Page 5: Matrix Operations. Matrix Notation Example Equality of Matrices

Square Matrix

Page 6: Matrix Operations. Matrix Notation Example Equality of Matrices

Diagonal Matrix

Page 7: Matrix Operations. Matrix Notation Example Equality of Matrices

Triangular Matrices

Page 8: Matrix Operations. Matrix Notation Example Equality of Matrices

Row and Column Vectors

Page 9: Matrix Operations. Matrix Notation Example Equality of Matrices

Transposition of Vectors

Page 10: Matrix Operations. Matrix Notation Example Equality of Matrices

Transposition of Matrices

Page 11: Matrix Operations. Matrix Notation Example Equality of Matrices

Example

Page 12: Matrix Operations. Matrix Notation Example Equality of Matrices

Symmetric and Skew-Symmetric Matrices

Page 13: Matrix Operations. Matrix Notation Example Equality of Matrices

Addition of Matrices

Page 14: Matrix Operations. Matrix Notation Example Equality of Matrices

Scalar Multiplication

Page 15: Matrix Operations. Matrix Notation Example Equality of Matrices

Zero Matrix

Page 16: Matrix Operations. Matrix Notation Example Equality of Matrices

Properties of Additon

Page 17: Matrix Operations. Matrix Notation Example Equality of Matrices

Properties of Scalar Multiplication

Page 18: Matrix Operations. Matrix Notation Example Equality of Matrices

Properties of Tranposition

Page 19: Matrix Operations. Matrix Notation Example Equality of Matrices

Product of Matricies

Page 20: Matrix Operations. Matrix Notation Example Equality of Matrices

Product of Matricies

Page 21: Matrix Operations. Matrix Notation Example Equality of Matrices

Identity Matrices

Page 22: Matrix Operations. Matrix Notation Example Equality of Matrices

Identity Property

Page 23: Matrix Operations. Matrix Notation Example Equality of Matrices

A System of Linear Equations

Page 24: Matrix Operations. Matrix Notation Example Equality of Matrices

The Matrix Equation Ax=b

Page 25: Matrix Operations. Matrix Notation Example Equality of Matrices

Properties of Matrix Multiplication

Page 26: Matrix Operations. Matrix Notation Example Equality of Matrices

Cautions

Page 27: Matrix Operations. Matrix Notation Example Equality of Matrices

Matrix Powers

Page 28: Matrix Operations. Matrix Notation Example Equality of Matrices

Theorem

Page 29: Matrix Operations. Matrix Notation Example Equality of Matrices

Properties of Transposition

Page 30: Matrix Operations. Matrix Notation Example Equality of Matrices

Definition of Linear Combination

Page 31: Matrix Operations. Matrix Notation Example Equality of Matrices

Consistency Theorem for Linear Systems

A linear system Ax=b is consistent if and only if b can be written as a linear combination of the column vectors of A.

Page 32: Matrix Operations. Matrix Notation Example Equality of Matrices

Definition

Page 33: Matrix Operations. Matrix Notation Example Equality of Matrices

Matrix Inverse Identities

So as an exercise in using this notation let’s look at The indices indicate very specific matrix or vector components/elements. These are not matrices

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