## Input Data for Matrix Calculators

*Now all matrix calculators support both real and complex matrices. To ensure that the browser loads the lastest calculators, it should be refreshed or reloaded.
Please send any comments and/or found bugs/errors to
dan@comnuan.com, last updated: May 27, 2016*

All matrix calculators require that the matrix entries must be entered as below.

Only matrix entries are entered and are in the form

1st row of matrix 2nd row of matrix ............ last row of matrix

The number of rows of the matrix is determined from the number of non-empty lines of the input and the number of columns is determined from the number of entries in the first row.

At least one white space is required to separate each matrix entry. Matrices can be copied and pasted or manually edited in the text area.

Valid matrix entries are real numbers like 1, 2/3, -34.15, 2.0e-3 or complex numbers in the form `a+b*i` like 2+3*i, 4, 5*i. Note that complex entries must not contain space. The matrix entries can also be
input as mathematical expressions like sin(0.5), exp(pi), 1/2+1/3, 2^3, (2+3*i)^5, exp(1-i). All supported math functions for both real and complex are list in the table below.

*Since spaces are used as the matrix entry separator, matrix entries must not contain space*. For examples, 2+3*i and sin(0.5) are valid input but 2 +3 *i, sin( 0.5 ) are not because they contain spaces. Here is an example of valid input for matrix calculators.

sin(pi/2) -2 3+i 5-i 2^3 -1 log(10^3) 1 1/2+2/4

As all matrix entries are evaluated before they are passed to matrix calculators *we can use some matrix calculators like
transpose calculator or
trace calculator (with one entry) as scientific calculators*.
Note that the first calculator transpose the evaluated values if the number of entries are greater than one.
For example, enter `1/2+exp(pi)-sqrt(e)`
in the transpose or trace calculators we get the output 21.9920. And enter `(1+sqrt(5))/2 4*atan(1)` in the transpose calculator we get the output

1.6180 3.1416i.e.

`(1+sqrt(5))/2 = 1.6180`and

`4*atan(1) = 3.14.16`. In the case of evaluating complex math expression, the transpose calculator both transpose and take complex conjugate the results. For example enter

`(2+3*i)^2`in the calculator we get

`-5-12*i`as the output. Taking complex conjugate of the output, we get

`-5+12*i`which is the value of

`(2+3*i)^2`

All math functions in table below support both real and complex entries.

function | description | example |
---|---|---|

e | A constant e=2.718281828459045 | - |

pi | A constant pi=3.141592653589793 | - |

i | A constant $i=\sqrt{-1}$ | 2+3*i |

abs | abs(x) the absolute value of x | abs(-2) |

sqrt | sqrt(x) the square root of x | sqrt(2+5*i) |

pow | pow(x,y) the power of x to y, the same as x^y | pow(3,2) or 3^2 |

exp | exp(x) the base-e exponential function of x | exp(3) |

log | log(x) the natural logarithm of x | log(2) |

sin | sin(x) the sine of x | sin(1.5) |

cos | cos(x) the cosine of x | cos(1.5) |

tan | tan(x) the tangent of x | tan(1.5) |

asin | asin(x) the inverse sine of x | asin(0.5) |

acos | acos(x) the inverse cosine of x | acos(0.5) |

atan | atan(x) the inverse tangent of x | atan(0.5) |

sinh | sinh(x) the hyperbolic sine of x | sinh(0.5) |

cosh | cosh(x) the hyperbolic cosine of x | cosh(0.5) |

tanh | tanh(x) the hyperbolic tangent of x | tanh(0.5) |