ChukMatrix - a Math Matrix calculator

Description:

ChukMatrix is a kind of toolbox for performing simple operations with algebraic matrices on JS;
Matrices are presented with TAMM (two-dimensional arrays matrix model);
For correct working your matrix must match this syntax:
let matrix = [[1, 0, 1], [0, 1, 0], [1, 0, 1]], where every new internal array is a new matrix row;
for better understanding you may write like this:

let matrix = [
[1, 0, 1],
[0, 1, 0],
[1, 0, 1]
]

Documentation:

1) checkValid(a): checks if the matrix is valid by comparing the amount of every row element with the first one;

if the matrix is valid, you may get some useful information like size and shape;
Example:

ChukMatrix.checkValid(matrix1)

Output:

This matrix is valid!
This matrix is 3x3
This matrix is square

2) checkValidDiff(a, b): checks if the matrices have the same size to perform additive operations;

Example:

ChukMatrix.checkValidDiff(matrix1, matrix)

Output:
Matrices are match!

3) minus(a, b) and plus(a, b): performing addition and substraction operations;

Example:

ChukMatrix.minus(matrix1, matrix2)

Output:

7,0,2
0,8,-5

4) selfMultiply(a, n): performs multiplying of each element of a matrix by n (number)

Example:

ChukMatrix.selfMultiply(matrix1, 2)

Output:

This matrix is valid!
This matrix is 3x3
This matrix is square
This matrix after multiplication:
3,-3,3
-6,0,6
9,15,-6

5) transpose(a): performs transposing of a matrix

Example:

ChukMatrix.transpose(a)

Output:

Matrix after transposing:
1,-2,3
-1,0,5
1,2,-2

6) multiply(a, b): multiplies the matrix a by the matrix b

Example:

ChukMatrix.multiply(matrix1, matrix2)

Output:

Result after multiplication:
27,9,-3
-24,-30,18
-6,42,-24

7) determ (a): counts the determiner of the matrix a

Example:

let matrix1 = [
 [1, 2, 3],
 [3, -1, 4],
 [1, 2, 4]
]
ChukMatrix.determ(matrix1)

Output: The determinator of this matrix is: -7

8) reverse (a): finds reversed to matrix to matrix a

Example:

ChukMatrix.reverse(matrix1)

Output:

det A = -2 * 2 * 1 + -1 * -3 * 0 + 4 * -1 * 1 - -1 * 2 * -1 - -2 * 0 * 1 - 1 * 4 * -3 = 2
The determiner of this matrix is: 2
Matrix after minoring:
2,-4,6
2,-3,5
2,-4,8
Matrix after transposing:
2,2,2
-4,-3,-4
6,5,8
Reversed matrix:
2/2,2/2,2/2
-4/2,-3/2,-4/2
6/2,5/2,8/2

9) kramer (a): applies the kramer method to the equasion

Example:

/*
 5x + y -3z = -2
 4x + 3y + 2z = 16
 2x - 3y + z = 17
*/

let matrix = [
   [5, 1, -3, -2],
   [4, 3, 2, 16],
   [2, -3, 1, 17]
 ]
ChukMatrix.kramer(matrix)

Output:

<Starting Kramer Method>
Processing...

Matrix without remnant: 
5,1,-3
4,3,2
2,-3,1

Remnant: -2,16,17

det = (5 * 3 * 1) + (2 * 1 * 2) + (4 * -3 * -3) - (2 * 3 * -3) - (5 * 2 * -3) - (1 * 4 * 1) = 99
determiner is: 99

-2,1,-3
16,3,2
17,-3,1

det = (-2 * 3 * 1) + (17 * 1 * 2) + (16 * -3 * -3) - (17 * 3 * -3) - (-2 * 2 * -3) - (1 * 16 * 1) = 297
determiner is: 297

5,-2,-3
4,16,2
2,17,1

det = (5 * 16 * 1) + (2 * -2 * 2) + (4 * -3 * 17) - (2 * 16 * -3) - (5 * 2 * 17) - (1 * 4 * -2) = -198
determiner is: -198

5,1,-2
4,3,16
2,-3,17

det = (5 * 3 * 17) + (2 * 1 * 16) + (4 * -2 * -3) - (2 * 3 * -2) - (5 * 16 * -3) - (17 * 4 * 1) = 495
determiner is: 495

det X = 297 / 99 = 3
det Y = -198 / 99 = -2 
det Z = 495 / 99 = 5   
Done!

Ending...