We will be creating a class which will be given a 2-D array when instantiated, and then implement various methods to perform operations on the 2-D array. public class Matrix { private double[][] matrix; private final int NUMROW; private final int NUMCOL; public Matrix(double[][] m) { } public String toString() { } public Matrix transposeMatrix() { } public Matrix getUpperDiagonal() { } public Matrix getLowerDiagonal() { } public Matrix getDiagonal () { } public Matrix getAntiDiagonal () { } public boolean isSquareMatrix() { } public boolean isIdentityMatrix () { } public boolean isEqual (Matrix m) { } public void main(String[] args) { }

1. Matrix(double[][] m) a. Initialize the NUMROW and NUMCOL variables. These are the row and column dimensions of m. b. The constructor should initialize the double[][] matrix. c. Do not assume the input to the constructor is a NxN matrix e.g. the constructor and other methods need to work on a 4x4 matrix or a 4x2 matrix

2. toString() a. returns a string value of the entire matrix. To receive full points, string must be in this form: Each value should have a comma and a space except the last one. There should be no space before the closing bracket. 4x4 matrix [0.0, 1.0, 2.0, 3.0 4.0, 5.0, 6.0, 7.0 8.0, 9.0, 10.0, 11.0 12.0, 13.0, 14.0, 15.0] 4x2 matrix [0.0, 1.0 2.0, 3.0 4.0, 5.0 6.0, 7.0]

3. Matrix transposeMatrix() a. Transpose should work for square and non-square matrices b. Returns the transpose of the instance field matrix as a new Matrix object c. Include these two matrices below in your test cases for this method. The transpose of a matrix is a new matrix whose rows are the columns of the original. (This makes the columns of the new matrix the rows of the original). Here is a matrix and its transpose: Another way to look at the transpose is that the element at row r column c in the original is placed at row c column r of the transpose. The element arc of the original matrix becomes element acr in the transposed matrix.

4. Matrix getLowerDiagonal() and Matrix getUpperDiagonal() a. The getLowerDiagonal() should return a new matrix where all values below the main diagonal are 0. For example, given the following 4x4 matrix: 4x4 matrix [3.0, 1.0, 2.0, 3.0 4.0, 5.0, 6.0, 7.0 8.0, 9.0, 1.0, 1.0 1.0, 1.0, 1.0, 1.0] It should return the following as output: 4x4 matrix [3.0, 1.0, 2.0, 3.0 0.0, 5.0, 6.0, 7.0 0.0, 0.0, 1.0, 1.0 0.0, 0.0, 0.0, 1.0] b. Likewise, for getUpperDiagonal() removes all values above the main diagonal are 0. For example, given the following 4x4 matrix: 4x4 matrix [3.0, 1.0, 2.0, 3.0] [4.0, 5.0, 6.0, 7.0] [8.0, 9.0, 1.0, 1.0] [1.0, 1.0, 1.0, 1.0] It should return the following as output: 4x4 matrix [3.0, 0.0, 0.0, 0.0 4.0, 5.0, 0.0, 0.0 8.0, 9.0, 1.0, 0.0 1.0, 1.0, 1.0, 1.0] c. The main diagonal of a matrix (square or non-square) are when the indices in the matrix i and j are such that i = j.

5. Matrix getDiagonal() a. A diagonal matrix is a matrix where all values are 0 except the main diagonal b. Using only getLowerDiagonal() and getUpperDiagnoal(), return a diagonal matrix of the instance field matrix

6. Matrix getAntiDiagonal() a. An anti-diagonal matrix is a matrix where all values are 0 except the antidiagonal. The anti-diagonal is the diagonal doing from lower left corner to the upper right corner. b. returns an anti-diagonal matrix of the instance field matrix

7. boolean isSquareMatrix() a. returns true if the instance field matrix is a square matrix i.e., NUMROW is equal to NUMCOL; otherwise returns false

8. boolean isIdentityMatrix() a. returns true if the instance field matrix is an identity matrix; otherwise returns false. An identity matrix is always a square matrix with ones along the main diagonal and zeros elsewhere. b. Use isSquareMatrix(), getDiagonal() and isEqual methods only.

9. boolean isEqual (Matrix m) a. returns true if the instance field matrix is equal to given matrix m. The matrices will be equal if they have the same number of rows and columns and every value is also equal; otherwise return false