4.7 The Matrix ADT

In mathematics, a matrix is an $m � n$ rectangular grid or table of numerical values divided into $m$ rows and $n$ columns. Matrices, which are an important tool in areas such as linear algebra and computer graphics, are used in a number of applications, including representing and solving systems of linear equations. The Matrix ADT is defined next.

The Matrix ADT

A matrix is a collection of scalar values arranged in rows and columns as a rectangular grid of a fixed size. The elements of the matrix can be accessed by specifying a given row and column index with indices starting at 0.

Matrix(nrows, ncols)

Creates a new matrix containing nrows and ncols with each element initialized to 0. Both of the nrows and ncols parameters must be greater than 0, but at most one of them can be 0.
numRows()

Returns the number of rows in the matrix.
numCols()

Returns the number of columns in the matrix.
getitem(row, col)

Returns the value stored in the given matrix element. Both row and col must be within the valid range.
setitem(row, col, scalar)

Sets the matrix element at the given row and col to scalar. The element indices must be within the valid range.
scaleBy(scalar)

Multiplies each element of the matrix by the given scalar value. The matrix is modified by this operation.
transpose()

Returns a new matrix that is the transpose of this matrix.
add(rhsMatrix)

Creates and returns a new matrix that is the result of adding this matrix to the given rhsMatrix. The size of the two matrices must be the same.
subtract(rhsMatrix)

The same as the add operation but subtracts the two matrices.
multiply(rhsMatrix)

Creates and returns a new matrix that is the result of multiplying this matrix to the given rhsMatrix. The two matrices must be of appropriate sizes as defined for matrix multiplication.

4.6 Implementing the MultiArray ADT

Chapter 4. Multi-Dimensional Arrays

4.8 Matrix Operations