Matrix elements


Matrix form of record of this square form
Result of multiplication

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}; \ quad x = \ begin {pmatrix} x_ {1} \\ x_ {2} \\ \ vdots \\ x_ {n} \ end {pmatrix}; \ quad b = \ begin {pmatrix} b_ {1} \\ b_ {2} \\ \ vdots \\ b_ {m} \ 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

Multiplication result

 

 

Multiplication result

 

Complex field calculation

Multiplication result

Good calculations !!

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