Talk Outline
   • Scalars, vectors and matrices
   • Vector and matrix calculations
   • Identity, inverse matrices & 
     determinants
   • Solving simultaneous equations
   • Relevance to SPM
Linear Algebra & Matrices, MfD 2009
                   Scalar
   • Variable described by a single 
     number
   e.g. Intensity of each voxel in an MRI scan
Linear Algebra & Matrices, MfD 2009
                                   Vector
    •  Not a physics vector (magnitude, direction)
    •  Column of numbers e.g. intensity of same 
       voxel at different time points
                        x1
                        x2
                             
                        x3
                             
Linear Algebra & Matrices, MfD 2009
                                Matrices
      •  Rectangular display of vectors in rows and 
         columns
      •  Can inform about the same vector intensity at 
         different times or different voxels at the same 
         time
      •  Vector is just a n x 1 matrix                   d      d       d 
           1    2 3              1    4                11      12      13
     A5 4 1               C2 7             Dd            d       d 
                                                      21      22      23
           6    7 4              3    8             d       d       d 
                                                      31      32      33
           Square (3 x 3) Rectangular (3 x 2)      d   : ith row, jth column
                                                       i j
           Defined as rows x columns (R x C)
Linear Algebra & Matrices, MfD 2009
                  Matrices in Matlab
     • X=matrix                                   1 2 3
                                                          
     • ;=end of a row                             4 5 6
                                                  7 8 9
                                                          
     • :=all row or column
     Subscripting – each element of a 
     matrix can be addressed with a pair         “Special” matrix 
     of numbers; row first, column second        commands:        0
                                                                    
     (Roman Catholic)                            •                0
                                                   zeros(3,1) = 0
                                                                    
                                                               1  1
                                                                   
     e.g.    X(2,3) = 6                                        1  1
                                               • ones(2) =       
                      7 8 9
             X(3, :) =                                          8 1 6
                                                                    
                         5                                    3 5 7
                          
             X( [2 3], 2) =                                         
                         8                     • magic(3) = 4 9 2
                          
             
Linear Algebra & Matrices, MfD 2009