194x Filetype PPT File size 1.63 MB Source: www.sjctni.edu
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 A5 4 1 C2 7 Dd 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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