Matrix elements 2 -1 0 -1 3 5 0 5 -2

 Matrix form of record of this square form

The calculation of the quadratic form is a fairly simple task, at least the descriptive part is primitive to impossibility and the calculation algorithm, when the matrix is ​​known, consists in calculating each of the elements according to the formula

$Q(x)=\sum _{{i,j=1}}^{n}a_{{ij}}x_{i}x_{j}$

Where, $a_{{ij}}$ - matrix element

$A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix}$

But everything is primitive, does not mean convenient, and it is easy to make mistakes when calculating a quadratic form. Our calculator will help you not to make mistakes in the calculations.

As with all calculators, a matrix can contain not only real numbers, but also complex ones.

When entering data, we have two fields:

the first is the matrix;

the second is a way to name each element.

If in the second field we write some sort of character (a, b, c ....) then each element will be named $a_{{ij}}, b_{{ij}}, c_{{ij}}$

Let's look at a few examples.

Enter the elements of the matrix with a space (you can start each row with a new line)

and get the following results

$\begin{pmatrix}x_{0} & x_{1} & x_{2} \\ \end{pmatrix}*\begin{pmatrix}1 & 1 & 2 \\ 1 & 3 & 0 \\ 2 & 0 & 1 \\ \end{pmatrix}*\begin{pmatrix}x_{0} \\ x_{1} \\ x_{2} \\ \end{pmatrix}=\\=(1)x_{0}^2}+(2)x_{0}x_{1}+(4)x_{0}x_{2}+(3)x_{1}^2}+(1)x_{2}^2}$

$\begin{pmatrix}a_{0} & a_{1} & a_{2} \\ \end{pmatrix}*\begin{pmatrix}2 & 2 & -1 \\ 2 & -5 & 3 \\ -1 & 3 & 8 \\ \end{pmatrix}*\begin{pmatrix}a_{0} \\ a_{1} \\ a_{2} \\ \end{pmatrix}=\\=(2)a_{0}^2}+(4)a_{0}a_{1}+(-2)a_{0}a_{2}+(-5)a_{1}^2}+(6)a_{1}a_{2}+(8)a_{2}^2}$

Complex field calculation

$\begin{pmatrix}s_{0} & s_{1} & s_{2} & s_{3} \\ \end{pmatrix}*\begin{pmatrix}i & 4 & 2-i & -2 \\ -i & 2 & 2-i & i+7 \\ 2i-9 & 0.4-i & 11 & -6 \\ 1 & 0 & -i & 2i \\ \end{pmatrix}*\begin{pmatrix}s_{0} \\ s_{1} \\ s_{2} \\ s_{3} \\ \end{pmatrix}=\\=(i)s_{0}^2+(4-1i)s_{0}s_{1}+(-7+1i)s_{0}s_{2}+(-1)s_{0}s_{3}+(2)s_{1}^2+(2.4-2i)s_{1}s_{2}+(7+1i)s_{1}s_{3}+(11)s_{2}^2+(-6-1i)s_{2}s_{3}+(2i)s_{3}^2$

Good calculations !!

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