14.2.5  Getting the parts of a matrix

Accessing rows of a matrix.

The rows of a matrix are the elements of a list, and can be accessed with indices using the postfix […] or the prefix at (see Section 6.1.6). For example:

then:

or:

To extract a column of a matrix, you can first turn the columns into rows with transpose (see Section 15.1.1), then extract the row as above. For example:

or:

Individual elements are simply elements of the rows. For example:

This can be abbreviated by listing the row and column separated by a comma:

or:

The indexing begins with 0; you can have the indices start with 1 by enclosing them in double brackets.

Use a range (see Section 6.5.1) of indices to get submatrices. Some examples:

This gives you another way to extract a full column, by specifying all the rows as an index interval.

Recall that an index of −1 returns the last element of a list, an index of −2 the second to last element, etc.

Extracting rows or columns of a matrix (Maple compatibility).

The row (resp. col) command extracts one or several rows (resp. columns) of a matrix.

• row takes two arguments:
  • A, a matrix.
  • r, a row index or a range n₁,…,n₂.
• row(A,r) returns the row or sequence of rows given by r.
• col takes two arguments:
  • A, a matrix.
  • c, a column index or a range n₁,…,n₂.
• col(A,c) returns the column or sequence of columns given by c.

Examples

Extracting a sub-matrix of a matrix (TI compatibility).

The subMat command finds submatrices of a matrix.

• subMat takes one mandatory argument and four optional arguments:
  • A, a matrix.
  • Optionally, r₁, an integer, the row index for the beginning of the submatrix (by default, r₁=0).
  • Optionally, c₁, an integer, the column index for the beginning of the submatrix (by default, c₁=0).
  • Optionally, r₂, an integer, the row index for the end of the submatrix (by default, r₂ equals one less than the number of rows of A).
  • Optionally, c₂, an integer, the column index for the end of the submatrix (by default, c₁ equals one less than the number of columns of A).
• subMat(A ⟨,r₁,c₁,r₂,c₂⟩) returns the sub-matrix of A from position (r₁,c₁) to (r₂,c₂).

Examples

or:

or:

or: