1. Vlachopoulos Georgios Lecturer of Computer Science and Informatics Technological Institute of Patras, Department of Optometry, Branch of Egion Lecturer of Biostatistics Technological Institute of Patras, Department of Physiotherapy, Branch of Egion Matrices in Matlab

2. Vlachopoulos Georgios  Matlab  (Matrix Laboratory) ◦ A powerful tool to handle Matrices

3. Vlachopoulos Georgios  A=[2,4,7]  B=[1:1:10]  C=[10:3:40]  D=[30:-3:0]  D1=[1:pi:100]  Length(D1)  D2=linspace(2,10,20)

4.  E=[1,2,3↲  4,5,6]  F=[1,2,3;4,5,6] G=[1;2;3] H=[1,2,3; 4,5] Vlachopoulos Georgios

5. X=2; H=[x,sin(pi/4), 3,2*x; sqrt(5), x^2,log(x),4] H1=[x,sin(pi/4), 3,2*x; sqrt(5), x^2,log(x),4; linspace(1,2,4)] Vlachopoulos Georgios

6.  Special functions zeros(2,4) zeros(2,2) zeros(2) ones(2,4) ones(2,2) ones(2) eye(2,2) eye(2) eye(2,4) Vlachopoulos Georgios

7.  Special functions rand (2,4) rand(2,2) rand(2) magic(3) hilb(3) Vlachopoulos Georgios

8.  +  -  *  /  \ .* ./ .\  ^ (base and exp)  inv  size Vlachopoulos Georgios

9.  Inner Product ◦ dot(array1,array2)  Cross Product ◦ cross(array1,array2) Vlachopoulos Georgios

10.  Every polynomial corresponds to an array with elements the coefficients of the polynomial Example f1(x)=x 2 -5x+6  f1=[1,-5,6] f2(x)=x3-5x+6  f2=[1,0,-5,6] Vlachopoulos Georgios

11.  Add polynomials ◦ array1+array2 ◦ If we have different order polynomials we create equal sizes arrays adding zeros on missing coefficients  Add polynomials ◦ array1-array2 ◦ If we have different order polynomials we create equal sizes arrays adding zeros on missing coefficients  Multiply polynomials ◦ conv(array1,array2)  Divide polynomials ◦ deconv(array1,array2) Vlachopoulos Georgios

12.  Roots of a polynomial roots(array)  Polynomial with roots the elements of the array poly(array)  First order derivative of the Polynomial polyder(array)  Value of the Polynomial p for x=a polyval(p,a) Vlachopoulos Georgios

13.  Examples k1=root(f1) k2=root(f2) poly(k1) kder=polyder(f2) polyval(s2,5) Vlachopoulos Georgios

14.  A∪B  union(array1,array2)  A∩B  intersect(array1,array2)  A∼B  setdiff(array1,array2) Example ◦ a=1:6 ◦ b=0:2:10 ◦ c=union(a,b) ◦ d=intersect(a,b) ◦ e1=setdiff(a,b) ◦ e2=setdiff(b,a) Vlachopoulos Georgios

15.  Unique Elements  unique(array)  Elements of A that are members of B  ismember(array1,array2) Example ◦ f1=ismember(a,b) ◦ f2=ismember(b,a) ◦ g=[1,1,2,2,3,3] ◦ h=unique(g) Vlachopoulos Georgios

16.  Arrays ◦ Sum of array elements  sum(array) ◦ Product of array elements  prod(array) ◦ Cumulative sum of an array elements  cumsum(array) ◦ Cumulative prod of an array elements  cumprod(array) Vlachopoulos Georgios

17.  Matrices ◦ Sum of elements of each matrix column  sum(matrix) or  sum(matrix,1) ◦ Sum of elements of each matrix row  sum(matrix,2) Overall sum???? Vlachopoulos Georgios

18.  Matrices ◦ Product of elements of each matrix column  prod(matrix) or  prod(matrix,1) ◦ Product of elements of each matrix row  prod(matrix,2) Overall product???? Vlachopoulos Georgios

19.  Matrices ◦ Cumulative sum per column  cumsum(matrix) or  cumsum (matrix,1) ◦ Cumulative sum per row  cumsum (matrix,2) Vlachopoulos Georgios

20.  Matrices ◦ Cumulative sum per column  cumprod(matrix) or  cumprod (matrix,1) ◦ Cumulative sum per row  cumprod(matrix,2) Vlachopoulos Georgios

21.  Matrix element  A(i,j) Example: A=[1,2,3;4,5,6] A(2,1)↲ A(2,1)=4 Vlachopoulos Georgios

22. Example: A=[1,2,3;4,5,6;3,2,1] B=A(1:2,2,3) y=A(:,1) Z=A(1,:) W=A([2,3],[1,3]) A(:) Vlachopoulos Georgios

23.  Delete elements Example ◦ Clear all; ◦ A=magic(5) ◦ A(2,: )=[] % delete second row ◦ A(:[1,4])=[] % delete columns 1 and 4 ◦ A=magic(5) ◦ A(1:3,:)=[] % delete rows 1 to 3 Vlachopoulos Georgios

24.  Replace Elements Example ◦ Clear all; ◦ A=magic(5) ◦ A(2,3 )=5 % Replace Element (2,3) ◦ A(3,:)=[12,13,14,15,16] % replace 3 rd row ◦ A([2,5]=[22,23,24,25,26; 32,33,34,35,36] Vlachopoulos Georgios

25.  Insert Elements Example ◦ Clear all; ◦ A=magic(5) ◦ A(6,:)=[1,2,3,4,5,6] ◦ A(9,:)=[11,12,13,14,15,16] Vlachopoulos Georgios