Introduction to Matrices

1
Introduction to Matrices

• ME-190
• Jan. 2004
• Dr. W. Farrow

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Square Matrix

• Order 3 x 3 (since m n it can be written 3)
• Matlab definition
• A a11 a12 a13 a21 a22 a23 a31 a32 a33

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Column Matrix (Column Vector)

• Order 3 x 1
• Matlab definition
• A a11 a21 a31

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Row Matrix (Row Vector)

• Order 1 x 3
• Matlab definition
• A a11 a12 a13

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General Matrix Form

• Order m x n (m - of rows, n - of
  columns)
• Matlab definition
• A a11 a12 a1n a21 a22 a2n a31 a32 a3n
  
• am1 am2 amn

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Zero Matrix

• Order m x n (m - of rows, n - of
  columns)
• Matlab definition
• A zeros(m, n)

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Square Zero Matrix

• Order n ( for this example 3)
• Matlab definition
• A zeros(n)

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Ones Matrix

• Order m x n (m - of rows, n - of
  columns)
• Matlab definition
• A ones(m, n)

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Random Number Matrix

• Fills the matrix with random numbers 0 lt a lt 1
• Order m x n (m - of rows, n - of
  columns)
• Matlab definition
• A rand(m, n)

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Identity Matrix

• Order n ( for this example 3)
• Matlab definition
• A eye(n)

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System of Linear Equations

• A matrix can be used to represent a system of
  Linear equations
• a11 x1 a12 x2 a13x3 b1
• a21 x1 a22 x2 a23x3 b2
• a31 x1 a32 x2 a33x3 b3
• A X B

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Matrix Representation ofa System of Linear
Equations

• AX B

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Array Operationsvs Matrix Operations

• Addition Subtraction
• Same for both Arrays and Matrices
• Add corresponding elements
• Both must have same order

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Array Operationsvs Matrix Operations

• Addition Subtraction
• MatLab syntax
• C A B or C A - B

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Array Operationsvs Matrix Operations

• Multiplication of Arrays .
• Different than for Matrices
• Multiply corresponding elements
• Both must have same order or one must be scalar

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Array Operationsvs Matrix Operations

• Multiplication of Matrices (linear algebraic
  operation)
• Multiply elements of rows in matrix on left, with
  corresponding elements of column in matrix on
  right, sum the results and place in new matrix
• The matrices must be conformable or one must be
  scalar