Financial Toolbox

Adding and Subtracting Matrices

Matrix addition and subtraction operate element-by-element. The two input matrices must have the same dimensions. The result is a new matrix of the same dimensions where each element is the sum or difference of each corresponding input element. For example, consider combining portfolios of different quantities of the same stocks ("shares of stocks A, B, and C [the rows] in portfolios P and Q [the columns] plus shares of A, B, and C in portfolios R and S").

• Portfolios_PQ = [100   200
                   500   400
                   300   150];
  
  Portfolios_RS = [175   125
                   200   200
                   100   500];
  
  NewPortfolios = Portfolios_PQ + Portfolios_RS
  
  NewPortfolios =
  
          275.00        325.00
          700.00        600.00
          400.00        650.00
  

Adding or subtracting a scalar and a matrix is allowed and also operates element-by-element.

• SmallerPortf = NewPortfolios-10
  
  SmallerPortf =
          265.00        315.00
          690.00        590.00
          390.00        640.00
  

Matrix Algebra Refresher

Multiplying Matrices