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Philosophiae Naturalis Principia Matlab ematica

Philosophiae Naturalis Principia Matlab ematica. Damian Gordon. Getting to Matlab. Magic Matrix. MAGIC Magic square. MAGIC(N) is an N-by-N matrix constructed from the integers 1 through N^2 with equal row, column, and diagonal sums.

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Philosophiae Naturalis Principia Matlab ematica

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  1. Philosophiae Naturalis Principia Matlabematica Damian Gordon

  2. Getting to Matlab

  3. Magic Matrix MAGIC Magic square. MAGIC(N) is an N-by-N matrix constructed from the integers 1 through N^2 with equal row, column, and diagonal sums. Produces valid magic squares for N = 1,3,4,5,...

  4. Identity Function >> eye (4) ans = 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1

  5. Upper Triangle Matrix » triu(a) ans = 1 1 1 1 1 0 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 0 1 » a = ones(5) a = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

  6. Lower Triangle Matrix » tril(a) ans = 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 » a = ones(5) a = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

  7. Hilbert Matrix » hilb(4) ans = 1.0000 0.5000 0.3333 0.2500 0.5000 0.3333 0.2500 0.2000 0.3333 0.2500 0.2000 0.1667 0.2500 0.2000 0.1667 0.1429

  8. Inverse Hilbert Matrix » invhilb(4) ans = 16 -120 240 -140 -120 1200 -2700 1680 240 -2700 6480 -4200 -140 1680 -4200 2800

  9. Toeplitz matrix. TOEPLITZ TOEPLITZ(C,R) is a non-symmetric Toeplitz matrix having C as its first column and R as its first row. TOEPLITZ(R) is a symmetric (or Hermitian) Toeplitz matrix. -> See also HANKEL

  10. Summary of Functions • magic • eye(4) • triu(4) • tril(4) • hilb(4) • invhilb(4) • toeplitz(4) - magic matrix - identity matrix - upper triangle - lower triangle - hilbert matrix - Inverse Hilbert matrix - non-symmetric Toeplitz matrix

  11. Dot Operator • A = magic(4); b=ones(4); • A * B • A.*B • the dot operator performs element-by-element operations, for “*”, “\” and “/”

  12. Concatenation • To create a large matrix from a group of smaller ones • try • A = magic(3) • B = [ A, zeros(3,2) ; zeros(2,3), eye(2)] • C = [A A+32 ; A+48 A+16] • Try some of your own !!

  13. Subscripts • Row i and Column j of matrix A is denoted by A(i,j) • A = Magic(4) • try • A(1,4) + A(2,4) + A(3,4) + A(4,4) • try • A(4,5)

  14. The Colon Operator (1) • This is one MatLab’s most important operators • 1:10 means the vector • 1 2 3 4 5 6 7 8 9 10 • 100:-7:50 • 100 93 86 79 72 65 58 51 • 0:pi/4:pi • 0 0.7854 1.5708 2.3562 3.1416

  15. The Colon Operator (2) • The first K elements in the jth column is • A(1:K, j) • Sum(A(1:4, 4)) is the sum of the 4th column or • Sum(A(:, 4)) means the same

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