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
• Addition is done term by term • Example

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## This note was uploaded on 02/06/2011 for the course CHE 110A taught by Professor Mccurdy during the Fall '09 term at UC Davis.

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Vector_matrices - Vectors and Matrices Linear equations can...

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