If n = 0 this returns the identity matrix whose dimensions
match those of M.
If n = 1 this just returns M.
If n = -1 this returns inverse of M if it exists.
If n is a positive integer this multiplies M by itself
n times.
If n is a negative integer this multiplies the inverse of M
by itself n times.
M is square.
n is a dimensionless integer.
You can evaluate matrix powers symbolically. To do so:
Select the expression to evaluate.
Choose Simplify from the Symbolics menu.
Keystroke: -A
Returns an array the same size as A containing the negative of each element of A. It is equivalent to multiplying A by -1.
A is an array
Keystroke: [
This returns the nth element of v. If v has no nth element, you'll see an appropriate error message.
v is a vector (an array with one
column).
n is a dimensionless integer.
Keep in mind that all arrays start at 0 by default, not 1. For a vector with 10 elements, n must run between 0 and 9. To change this, choose Options / Built-In Variables tab from the Math menu and change ORIGIN.
Use subscripts when graphing vectors.
Keystroke: [
This returns the mnth element of M. If M has no mnth element, you'll see an appropriate error message.
M is an array.
m and n must be dimensionless integers.
Keep in mind that all arrays start at 0 by default, not 1. For a matrix with 10 rows and 5 columns,
m must run between 0 and 9
n must run between 0 and 4
To change this, choose Options from the Math menu and click on the Built-In Variables tab in the Math Options dialog box. Change the ORIGIN.
This represents the starting index of all arrays. To change it, choose Options / Built-In Variables tab from the Math menu.
You can set ORIGIN to any integer, positive or negative. The value you set for ORIGIN will affect every array in your worksheet.
Keystroke: -
A - B
Subtracts the elements of B from the corresponding elements of A. A and B must have the same number of rows and columns.
A - x
If A is an array and x is a scalar then A - x is an array formed by subtracting x from every element in A.
A and B are matrices having the
same number of rows and columns.
x is a scalar.
Keystroke: Ctrl+6
Returns the nth column of the array M. If M has no nth column, you'll see an appropriate error message.
M must be an array
n is a scalar. It may not be complex
Keep in mind that all arrays start at 0 by default, not 1. For a matrix with 10 columns, n must run between 0 and 9. To change this, choose Options / Built-in Variables tab from the Math menu and change ORIGIN.
To get a row from a matrix, use this in conjunction with the transpose operator. For example, to get the first row from a matrix M, type M Ctrl+1 Ctrl+6 1.
Keystroke: Ctrl+1
This returns the n x m array formed by interchanging rows and columns of an m x n array.
M is an m x n array.
Although you can use the matrix transpose operator to find matrix transposes numerically, you can also find matrix transposes symbolically.
Keystroke: Ctrl+-
Changes the meaning of operators and functions so that they apply to every element of an array. This allows you to perform calculations in parallel.
A and B are arrays with the same
number of rows and columns.
To vectorize an expression,
1. Place the expression between the editing lines.
2. Press Ctrl+-.
To perform matrix multiplication of A and B, you would see
To multiply each element of A by the corresponding element in B.
Many functions and operators automatically perform operations on the elements of arrays so you do not always have to use the vectorize operator. Use the vectorize operator primarily when a function or operator has a special meaning for arrays. For instance, in the examples above, multiplication has a special meaning for arrays and that meaning is used by default. The vectorize operator has to be used to force an element-by-element multiplication.
Keystroke: Ctrl+4
v
Returns the sum of all the elements in the vector v.
v
is a vector.
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