Matrix Multiplication and Related Operations

Return to List of Lectures

Previous Lecture

• Misc
  • Math dept scholarship applications available
    • See notice on dept home page, http://www.geneseo.edu/math/home
  • Colloquia
    • Dawood, “Mathematical Methods in Equity Research”
      • Thursday, February 19, 3:00 - 4:00, Newton 203
    • Dickerson, “Mathematics Majors’ Understandings of the Concept of Mathematical Definition”
      • Monday, February 23th, 4:00-5:00, Newton 201
    • Extra credit for summaries
• Questions?
• Plotting Lab?
• 3D Plotting Project
  • Handout
• Matrix Multiplication
  • Section 2.4
    • A × B multiplies rows of A by columns of B element-by-element and adds up products to elements of C
    • Inner dimensions (number of columns in A and rows in B) have to be same
    • Product has number of rows of A and number of columns of B
    • Order matters: not commutative
    • Can apply to vectors of same length if one is row and other is column
    • Matlab
      • * mutiplies matrices
      • Also ^ to multiply matrix by itself repeatedly and \ to solve systems of equations in matrix form
    • Also dot and cross products
      • Dot product produces number
      • Cross product only for 3-element vectors
  • Examples
    

    >> A = [ 1 2; 3 4]
    A =
        1     2
        3     4
    >> B = [1 2 3;10 20 30]
    B =
         1     2     3
        10    20    30
    >> A*B
    ans =
        21    42    63
        43    86   129
    >> B*A
    Error using  * 
    Inner matrix dimensions must agree.
    >> A* [ 10 20; 30 40 ]
    ans =
        70   100
       150   220
    
    >> [ 1 0; 0 1] * A
    ans =
        1     2
        3     4
    >> eye(10)
    ans =
        1     0     0     0     0     0     0     0     0     0
        0     1     0     0     0     0     0     0     0     0
        0     0     1     0     0     0     0     0     0     0
        0     0     0     1     0     0     0     0     0     0
        0     0     0     0     1     0     0     0     0     0
        0     0     0     0     0     1     0     0     0     0
        0     0     0     0     0     0     1     0     0     0
        0     0     0     0     0     0     0     1     0     0
        0     0     0     0     0     0     0     0     1     0
        0     0     0     0     0     0     0     0     0     1
    >> A = [ 2 1; 1 -2 ]
    A =
        2     1
        1    -2
    >> B = [5 -1]
    B =
        5    -1
    >> A \ B
    Error using  \ 
    Matrix dimensions must agree.
    >> B = B'
    B =
        5
       -1
    >> A \ B
    ans =
        1.8000
        1.4000

• Next
  • Matrix lab

Next Lecture