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picture1_Algebra Powerpoint 74979 | Linear Algebra And Matrices


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File: Algebra Powerpoint 74979 | Linear Algebra And Matrices
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 ...

icon picture PPT Filetype Power Point PPT | Posted on 01 Sep 2022 | 3 years ago
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                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
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...Talk outline scalars vectors and matrices vector matrix calculations identity inverse determinants solving simultaneous equations relevance to spm linear algebra mfd scalar variable described by a single number e g intensity of each voxel in an mri scan not physics magnitude direction column numbers same at different time points x rectangular display rows columns can inform about the times or voxels is just n d c dd square ith row jth i j defined as r matlab end all subscripting element be addressed with pair special first second commands roman catholic zeros ones magic...

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