Vector_matrices

# Vector_matrices - Vectors and Matrices Linear equations can...

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Vectors and Matrices Linear equations can be conveniently represented using matrices and vectors A vector is an ordered list of numbers A matrix is a rectangular array of numbers

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Matrices The set of (m x n) real matrices is noted • Example
Matrix arithmetic Addition is done element by element Example in Addition is commutative: A+B=B+A

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Matrix multiplication Matrix multiplication is defined by The dimensions of A and B must be compatible
Matrix multiplication Example with i th row of A j th column of B

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Matrix multiplication • Example
Matrix multiplication Matrix multiplication is not commutative Even if A*B is defined, B*A may not be defined – If A and B have compatible dimensions, this does not mean that B and A have compatible dimensions – Example:

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Matrix transposition The transpose A T of a matrix A is defined by • Example
Vectors • A column vector in is an ordered list of m numbers • Example: m=4

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Vectors • A row vector in is a (1 x n) matrix • If x is a column vector, its transpose x T is a row vector
Vector arithmetic Addition is done term by term • Example

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Vector arithmetic Multiplication by a scalar • Example
Scalar product The scalar (inner) product of two vectors is defined by

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