aug

Returns a matrix with a new column added.

Syntax

• aug(A, v)

  • A is a matrix

  • v is a vector

• aug(A, B)

  • A is a matrix

  • B is a matrix

Description

If A is a matrix of size m×n and v an m-dimensional vector, then aug(A, v) returns the matrix obtained from A by appending v to it as a new rightmost column.

More generally, if A and B are matrices with the same number of rows, then aug(A, B) returns the matrix obtained by putting them next to each other, with A to the left and B to the right.

If A or B above is not a matrix but a vector, it is treated like a single-column matrix. If A, B, or v is a number, it is treated like a single-entry matrix.

Examples

aug(IdentityMatrix(3), ZeroVector(3))

⎛1  0  0  0⎞
⎜0  1  0  0⎟
⎝0  0  1  0⎠

3⋅aug(IdentityMatrix(3), HilbertMatrix(3))

⎛   3     0     0     3   1.5     1⎞
⎜   0     3     0   1.5     1  0.75⎟
⎝   0     0     3     1  0.75   0.6⎠

See also

• lessen