The .^ Command


Command Summary

Raises a value to a power, doing this element-by-element for matrices.

Command Syntax

base .^ exponent

Menu Location

  • Press 2nd MATH to enter the MATH menu.
  • Press 4 to enter the Matrix submenu.
  • Press K to enter the Element ops submenu.
  • Press 1 to select .+.

…frankly, just typing it is way easier.

Calculator Compatibility

This command works on all calculators.

Token Size

1 byte

The .^ operator is generally the same as ^, except when dealing with matrices. While ^ does quite a lot of matrix-specific stuff (check out its page for more information), .^ just applies it element-by-element:

:[a,b;c,d] .^ 2
           [a^2  b^2]
           [c^2  d^2]

The command can handle any choice of matrix and scalar as the base and exponent. However, if you're raising a constant number to a matrix power, be careful that the dot in .^ is not confused for a decimal point, by adding extra spaces:

           Error: Data type
:2 .^ [a,b;c,d]
           [2^a  2^b]
           [2^c  2^d]

Although this doesn't come up often, be aware that .^, like ^, is evaluated from right to left: a.^b.^c is calculated as a.^(b.^c), not as (a.^b).^c.

Error Conditions

240 - Dimension mismatch happens when a matrix is raised to the power of another matrix, with different dimensions.

Related Commands

See Also

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