MATRIX ALGEBRA Matrix Algebra 4 pi ar cs i mi riy fif nkp bxrsR A=[NA]=[Alk NNM Ii=laai k= li((K whxrxi txnfiaxs ahx rfiw nkp bxnint h txnfiaxs ahx Ciikp ml xFafir 4 pi ar wah finy fix EEkp m Example 5 N Rfw lxPafir 4 piard wah fimy fix rfw Example 6 Sypp xandEr iar5(Nk= Ni Example 7 2 A=21 321 Da gini3pia(Nk=0I≠k) Example 8 100 020 SFiSnpiar(Nk=OI Ni=NkIifh Example 9 300 It xmaay piaG5 (N:=OI Ni= Nk=1I ithMATRIX ALGEBRA 3 Matrix Algebra A matrix is an array of numbers, A = [aik] = [A] ik =      a11 a12 · · · a1K a21 a22 · · · a2K · · · an1 an2 · · · anK      , i = 1, ..., n, k = 1, ..., K where i denotes the row number and k denotes the column number. Column vector: A matrix with only one column. Example 5 vi =       a1 a2 . . . an       Row vector: A matrix with only one row Example 6 vk =  a1 a2 · · · aK Symmetric matrix (aik = aki) Example 7 A =    1 2 3 2 1 2 3 2 1    Diagonal matrix (aik = 0, i = k) Example 8 A =    1 0 0 0 2 0 0 0 3    Scalar matrix (aik = 0, aii = akk, i = k) Example 9 A =    3 0 0 0 3 0 0 0 3    Identity matrix (aik = 0, aii = akk = 1, i = k)