Matrix Calculator

Free online calculator for matrices and complex numbers. Quickly calculate a range of linear algebra values, including matrix determinants, inverses and cofactor matrices. Includes support for complex matrices, and extensive functions of complex numbers (trigonometry, hyperbolic trigonometry etc.).

You can easily generate the LaTeX code for any equation, including matrices, square roots and greek letters.

Quick Start:

Automatically convert greek letters
Format output numbers
Decimal Places
Copy as LaTeX
Conjugate Style zz^*
Default Matrix Zero Identity
Allow scientific notation

Equations are entered in the usual manner and the result is updated as you type. To add an exponent press ^ and for a subscript press _.

Numbers can be entered in scientific notation (eg: 1e3 for 1000). This can be disabled in the settings menu.

The output of a calculation can be assigned to a variable by naming it in the box next to the output. If you change the equation all subsequent calculations that use that variable will automatically update unless you disable this in the settings menu.

Matrices

To add a matrix either click the button in the controls or press Ctrl + M. You can then resize the matrix by clicking on and dragging the icon in the lower right corner. The size of the matrix will be displayed whilst you are resizing.

The following linear algebra functions are supported:

adj (also as adjugate or adjoint)
cofactor
det
trace
transpose

Matrix determinants are calculated using the Laplace expansion. When taking the determinant of just one matrix the brackets with be automatically replaced with the modulus bars. To add something before/after the matrix move to the first/last cell and move left/right.

Vectors

Vectors can be added by clicking the button in the control panel, or by resizing an existing matrix so that it only has 1 column.

Cross product is set using the usual multiplication operation (*). Both vectors are required to be three dimensional.

The dot product can be added from the button on the onscreen keyboard. The vectors can be any size as long as they are both the same size. The dot product for vectors containing complex numbers is calculated with the conjugate of the second vector.

proj_b(a) calculates the projection of the vector a onto a named vector b. The named vector must be set as a variable. To type the subscript press _. There is also oproj_b(a) which calculates the orthogonal projection.

General

abs
ceil - round up
floor - round down
log
round
sign

The default base for the log function is e. To use a different base add any number is a subscript after the log (eg: log₁₀(100)).

Trigonometry

All trigonometry functions support both real and complex arugments. You can set the trigonometric functions to work in degrees or radians from the options on the keyboard, but this will only work for real numbers. The following functions are supported:

cos
sin
tan
cot
sec
csc

There are also the inverse functions:

cos^-1 (also acos and arccos)
sin^-1 (also asin and arcsin)
tan^-1 (also atan and arctan)
cot^-1 (also acot and arccot)
sec^-1 (also asec and arcsec)
csc^-1 (also acsc and arccsc)

A square exponent after the function name returns the square of the result of the function (e.g sin²(x) = (sin(x)²). For all other exponents use brackets and place the exponent afterwards.

Hyperbolic Trigonometry

As with the trigonometry functions, the hyperbolic trigonometry functions all work with both real and complex values.

cosh
sinh
tanh
coth
sech
csch
cosh^-1 also arccosh
sinh^-1
tanh^-1

Complex Numbers

Complex numbers can be used in any function that supports real numbers. By default complex numbers are inputted as either x + yi or x + yj. If you want to multiply two complex numbers they will need to have brackets.

There are also functions specific to complex numbers:

Arg
conj - the complex conjugate
Im
Re

When a function is multi-valued the result returned is in the principal value.

LaTeX

You can easily convert both the equation and the output to LaTeX from the options menu at the top right of each calculation box. Alternatively you can set it so that the default copy mode is LaTeX. There are a variety of settings for the LaTeX that are accessible on the LaTeX output box.

Matrices

Vectors

General

Trigonometry

Hyperbolic Trigonometry

Complex Numbers

LaTeX

LaTeX

Options

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