# Investing matrices matlab matrix

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Playing with time series matrices. Show older comments. Vote 0. Answered: Cam Salzberger on 3 Sep Hi all, I have a time series matrix ie : first column being a date, second a value of an investment and I wish to compute the daily returns. What's the formulae I should use in the command windows? Multiplying the 5 -by- 3 week's closing prices matrix by the 3 -by- 2 portfolios matrix yields a 5 -by- 2 matrix showing each day's closing value for both portfolios. Monday's values result from multiplying each Monday closing price by its respective number of shares and summing the result for the first portfolio, then doing the same for the second portfolio.

Tuesday's values result from multiplying each Tuesday closing price by its respective number of shares and summing the result for the first portfolio, then doing the same for the second portfolio. And so on, through the rest of the week. Multiplying a matrix by a scalar is an exception to the dimension and commutative rules. It just operates element-by-element.

Matrix division is useful primarily for solving equations, and especially for solving simultaneous linear equations see Solving Simultaneous Linear Equations. In formal matrix algebra, the solution involves matrix inversion. In general,. In general, matrix A must be a nonsingular square matrix; that is, it must be invertible and it must have the same number of rows and columns. Generally, a matrix is invertible if the matrix times its inverse equals the identity matrix.

To understand the theory and proofs, consult a textbook on linear algebra such as Elementary Linear Algebra by Hill listed in Bibliography. Matrix division is especially useful in solving simultaneous linear equations. Consider this problem: Given two portfolios of mortgage-based instruments, each with certain yields depending on the prime rate, how do you weight the portfolios to achieve certain annual cash flows?

The answer involves solving two linear equations. It is a linear equation because it describes a line in the xy -plane. A system of linear equations is a set of linear equations that you usually want to solve at the same time; that is, simultaneously. A basic principle for exact answers in solving simultaneous linear equations requires that there be as many equations as there are unknowns.

To get exact answers for x and y , there must be two equations. For example, to solve for x and y in the system of linear equations. Matrix algebra represents this system as an equation involving three matrices: A for the left-side constants, X for the variables, and B for the right-side constants. Solving the system simultaneously means solving for X. In general, you can use matrix algebra to solve any system of linear equations such as.

To illustrate, consider this situation. There are two portfolios of mortgage-based instruments, M1 and M2. An investor holds 10 units of M1 and 20 units of M2. As word equations:. Find the answer by solving two linear equations. The investor should hold Finally, element-by-element arithmetic operations are called operations. Addition and subtraction, and matrix multiplication and division by a scalar, are already array operations so no period is necessary. When using array operations on two matrices, the dimensions of the matrices must be the same.

For example, given vectors of stock dividends and closing prices. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:. Select the China site in Chinese or English for best site performance. Other MathWorks country sites are not optimized for visits from your location. Toggle Main Navigation.

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