#### Matrix Multiplication

```// Wikipedia URL for General Matrix Multiplication Concepts: https://en.wikipedia.org/wiki/Matrix_multiplication

// This algorithm has multiple functions that ultimately check if the inputs are actually matrices and if two Matrices (that can be different sizes) can be multiplied together.
// matrices that are of the same size [2x2]x[2x2], and the second is the multiplication of two matrices that are not the same size [2x3]x[3x2].

// MatrixCheck tests to see if all of the rows of the matrix inputted have similar size columns
const matrixCheck = (matrix) => {
let columnNumb
for (let index = 0; index < matrix.length; index++) {
if (index === 0) {
columnNumb = matrix[index].length
} else if (matrix[index].length !== columnNumb) {
// The columns in this array are not equal
} else {
return columnNumb
}
}
}

// tests to see if the matrices have a like side, i.e. the row length on the first matrix matches the column length on the second matrix, or vice versa.
const twoMatricesCheck = (first, second) => {
const [firstRowLength, secondRowLength, firstColLength, secondColLength] = [first.length, second.length, matrixCheck(first), matrixCheck(second)]
if (firstRowLength !== secondColLength || secondRowLength !== firstColLength) {
// These matrices do not have a common side
return false
} else {
return true
}
}

// returns an empty array that has the same number of rows as the left matrix being multiplied.
// Uses Array.prototype.map() to loop over the first (or left) matrix and returns an empty array on each iteration.
const initiateEmptyArray = (first, second) => {
if (twoMatricesCheck(first, second)) {
const emptyArray = first.map(() => {
return ['']
})
return emptyArray
} else {
return false
}
}

// Finally, `matrixMult` uses `Array.prototype.push()`, multiple layers of nested `for` loops, the addition assignment `+=` operator and multiplication operator `*` to perform the dot product between two matrices of differing sizes.
// Dot product, takes the row of the first matrix and multiplies it by the column of the second matrix, the `twoMatricesCheck` tested to see if they were the same size already.
// The dot product for each iteration is then saved to its respective index into `multMatrix`.
export const matrixMult = (firstArray, secondArray) => {
const multMatrix = initiateEmptyArray(firstArray, secondArray)
for (let rm = 0; rm < firstArray.length; rm++) {
const rowMult = []
for (let col = 0; col < firstArray.length; col++) {
rowMult.push(firstArray[rm][col])
}
for (let cm = 0; cm < firstArray.length; cm++) {
const colMult = []
for (let row = 0; row < secondArray.length; row++) {
colMult.push(secondArray[row][cm])
}
let newNumb = 0
for (let index = 0; index < rowMult.length; index++) {
newNumb += rowMult[index] * colMult[index]
}
multMatrix[rm][cm] = newNumb
}
}
return multMatrix
}

// const firstMatrix = [
//   [1, 2],
//   [3, 4]
// ]

// const secondMatrix = [
//   [5, 6],
//   [7, 8]
// ]

// matrixMult(firstMatrix, secondMatrix) // [ [ 19, 22 ], [ 43, 50 ] ]

// const thirdMatrix = [
//   [-1, 4, 1],
//   [7, -6, 2]
// ]
// const fourthMatrix = [
//   [2, -2],
//   [5, 3],
//   [3, 2]
// ]

// matrixMult(thirdMatrix, fourthMatrix) // [ [ 21, 16 ], [ -10, -28 ] ]
```  