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Many financial
analysis procedures involve *sets* of numbers;
for example, a portfolio of securities at various prices and yields.
Matrices, matrix functions, and matrix algebra are the most efficient
ways to analyze sets of numbers and their relationships. Spreadsheets
focus on individual cells and the relationships between cells. While
you can think of a set of spreadsheet cells (a range of rows and columns)
as a matrix, a matrix-oriented tool like MATLAB^{®} software manipulates
sets of numbers more quickly, easily, and naturally. For more information,
see Matrix Algebra Refresher.

**Matrix. **A rectangular array of numeric or algebraic quantities subject
to mathematical operations; the regular formation of elements into
rows and columns. Described as a "*m*-by-*n*"
matrix, with *m * the number of rows and *n * the
number of columns. The description is always "row-by-column."
For example, here is a `2`-by-`3` matrix
of two bonds (the rows) with different par values, coupon rates, and
coupon payment frequencies per year (the columns) entered using MATLAB notation:

Bonds = [1000 0.06 2 500 0.055 4]

**Vector. **A matrix with only one row or column. Described as a "`1`-by-*n*"
or "*m*-by-`1`"
matrix. The description is always "row-by-column." For
example, here is a `1`-by-`4` vector
of cash flows in MATLAB notation:

Cash = [1500 4470 5280 -1299]

To reference specific matrix elements, use (row, column) notation. For example:

Bonds(1,2)

ans = 0.06

Cash(3)

ans = 5280.00

You can enlarge matrices using small matrices or vectors as elements. For example,

AddBond = [1000 0.065 2]; Bonds = [Bonds; AddBond]

adds another row to the matrix and creates

Bonds = 1000 0.06 2 500 0.055 4 1000 0.065 2

Likewise,

Prices = [987.50 475.00 995.00] Bonds = [Prices, Bonds]

adds another column and creates

Bonds = 987.50 1000 0.06 2 475.00 500 0.055 4 995.00 1000 0.065 2

Finally, the colon (`:`) is important in generating and referencing
matrix elements. For example, to reference the par value, coupon rate,
and coupon frequency of the second bond:

BondItems = Bonds(2, 2:4)

BondItems = 500.00 0.055 4

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