Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[1/2*x^2 1/2*x^3]
[ x^4 x^5]
We try and fail to rescale a matrix over the integers by a non-integer:
sage: a = matrix(ZZ,2,3,[0,1,2, 3,4,4]); a
[0 1 2]
[3 4 4]
sage: a.rescale_row(1,1/2)
Traceback (most recent call last):
...
TypeError: Rescaling row by Rational Field element cannot be done over Integer Ring, use cha
To rescale the matrix by 1/2, you must change the base ring to the rationals:
sage: a = a.change_ring(QQ); a
[0 1 2]
[3 4 4]
sage: a.rescale_col(1,1/2); a
[ 0 1/2 2]
[ 3 2 4]
set_col_to_multiple_of_col(i, j, s)
Set column i equal to s times column j.
EXAMPLES: We change the second column to -3 times the first column.
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.set_col_to_multiple_of_col(1,0,-3)
sage: a
[ 0 0 2]
[ 3 -9 5]
If we try to multiply a column by a rational number, we get an error message:
sage: a.set_col_to_multiple_of_col(1,0,1/2)
Traceback (most recent call last):
...
TypeError: Multiplying column by Rational Field element cannot be done over Integer Ring, us
set_immutable()
Call this function to set the matrix as immutable.
Matrices are always mutable by default, i.e., you can change their entries using A[i,j] = x. However,
mutable matrices aren’t hashable, so can’t be used as keys in dictionaries, etc. Also, often when implementing
a class, you might compute a matrix associated to it, e.g., the matrix of a Hecke operator. If you
return this matrix to the user you’re really returning a reference and the user could then change an entry;
this could be confusing. Thus you should set such a matrix immutable.
EXAMPLES:
sage: A = Matrix(QQ, 2, 2, range(4))
sage: A.is_mutable()
True
sage: A[0,0] = 10
sage: A
[10 1]
[ 2 3]
88 Chapter 5. Base class for matrices, part 0