Linear Algebra | Matrices | Determinants | Equation Systems | Vectors

Calculator for Matrices

Matrices (singular matrix) are rectangular arrays of mathematical elements, like numbers or variables. Above all, they are used to display linear transformations. Here, it is calculated with matrix A and B, the result is given in the result matrix C. To continue calculating with the result, click Result to A or Result to B.

Matrix A rows: columns: | Matrix B rows: columns: | Decimal digits:

Matrix A			Matrix B
(		)	(		)

Result matrix C
(		)

with/by
Swap at with
with/by
Add at times to
Raise to the power of

The elements of the matrices are designated by index numbers. In matrix A, the elements of the first row are designated a₁₁, a₁₂, a₁₃ ... those of the second row are a₂₁, a₂₂, a₂₃, ... In matrix B, they are b₁₁, b₁₂, and so on. Each element has a numerical value, and these values are used for calculations.
Matrices can have a different number of columns and rows. In order to be able to calculate with two matrices, their sizes must match. Addition and subtraction with matrices is done by adding and subtracting the individual elements with the same index numbers of the matrices. So both matrices must be the same size. For A+B, the following applies to the result matrix C: c₁₁=a₁₁+b₁₁, c₁₂=a₁₂+b₁₂, ...
When multiplying A*B, the number of columns in matrix A must match the number of rows in matrix B, the other way around for B*A. The calculation is more complicated than that of addition and subtraction. Matrix multiplication is not commutative, A*B leads to different results than B*A.
Transposing means swapping the rows and columns of a matrix, the transposed matrix is written into the result matrix.
Result to A or B transfers the contents of the result matrix to one of the two upper ones. In a zero matrix, the values of all elements are zero. In a identity matrix, all elements are 0, except for a11=1, a22=1, a33=1, ... The identity matrix therefore has a slanting line of ones from top left to bottom right.
The two matrices A and B can be transferred to the calculators for the determinant and for the system of equations. Matrix C can be transferred to the data set and read out in its entirety. At Reading Data Set, data in text form can be transferred into a matrix.