Matrix Manipulation.sagews

# Share Link: https://cloud.sagemath.com/projects/026994b5-e264-4071-a9e1-127c5595f170/files/Matrix%20Manipulation.sagews
#
# Matrix arithmetic
#

#
# Define a matrix
#
int_mat = matrix([[1,2,3],[4,5,6]])
print "int_mat ="
print int_mat
print

#
# We use binary numbers instead of integers in UEET2533.
# Hence, declaring a binary (i.e. GF(2)) matrix
#
a_mat = matrix(GF(2), [[1,0,1], [0,1,0], [0,1,1]])
print "a_mat ="
print a_mat
print

# Transpose a matrix
print "a_mat.T =\n", a_mat.T
print

# Inverse a matrix
print "a_mat.I =\n", a_mat.I
print

# Sum matrix
b_mat = a_mat + a_mat.I
print 'a_mat * a_mat.I'
print b_mat
print


# Multiply matrix with *
b_mat = a_mat * a_mat.I
print 'a_mat * a_mat.I'
print b_mat
print

# Determinant
print 'a_mat.determinant() =', a_mat.determinant()
print

int_mat = [1 2 3] [4 5 6] a_mat = [1 0 1] [0 1 0] [0 1 1] a_mat.T = [1 0 0] [0 1 1] [1 0 1] a_mat.I = [1 1 1] [0 1 0] [0 1 1] a_mat * a_mat.I [0 1 0] [0 0 0] [0 0 0] a_mat * a_mat.I [1 0 0] [0 1 0] [0 0 1] a_mat.determinant() = 1

#
# Shortcut to create some special matrix.
#

# Define zero matrix
zero_mat = zero_matrix(GF(2), 4,4)
print 'zero_mat = zero_matrix(GF(2), 4,4)'
print zero_mat
print

# Define identity matrix
idn_mat = identity_matrix(GF(2), 4)
print 'idn_mat = identity_matrix(GF(2), 4)'
print idn_mat
print


# Random matrix
rand_mat = random_matrix(GF(2), 3, 3)
print 'rand_mat = random_matrix(GF(2), 3, 3)'
print rand_mat
print

zero_mat = zero_matrix(GF(2), 4,4) [0 0 0 0] [0 0 0 0] [0 0 0 0] [0 0 0 0] idn_mat = identity_matrix(GF(2), 4) [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] rand_mat = random_matrix(GF(2), 3, 3) [1 0 1] [1 0 1] [0 1 0]

#
# Manipulate matrices
#

a_mat = random_matrix(GF(2), 3, 4)
b_mat = identity_matrix(GF(2), 4)
c_mat = zero_matrix(GF(2), 3, 2)

print 'a_mat = \n', a_mat
print 'b_mat = \n', b_mat
print 'c_mat = \n', c_mat
print

#
print 'Stack matrices with: a_mat.stack(b_mat) '
print a_mat.stack(b_mat)
print

#
print 'Augment matrices with: a_mat.augment(c_mat)'
print a_mat.augment(c_mat)
print


#
print 'Reprint a_mat ='
print a_mat
print 'Get the first two columns of a_mat with: a_mat.matrix_from_columns(range(2))'
print a_mat.matrix_from_columns(range(2))
print

print 'Get the first two rows of a_mat with: a_mat.matrix_from_rows(range(2))'
print a_mat.matrix_from_rows(range(2))
print

print 'Remove the first row from a_mat with: a_mat.delete_rows([0])'
print a_mat.delete_rows([0])
print

print 'swap the first two rows of a_mat with: a_mat.swap_rows(0, 1)'
a_mat.swap_rows(0, 1)
print a_mat
print

a_mat = [0 1 0 1] [1 1 1 1] [0 1 1 1] b_mat = [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] c_mat = [0 0] [0 0] [0 0] Stack matrices with: a_mat.stack(b_mat) [0 1 0 1] [1 1 1 1] [0 1 1 1] [1 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] Augment matrices with: a_mat.augment(c_mat) [0 1 0 1 0 0] [1 1 1 1 0 0] [0 1 1 1 0 0] Reprint a_mat = [0 1 0 1] [1 1 1 1] [0 1 1 1] Get the first two columns of a_mat with: a_mat.matrix_from_columns(range(2)) [0 1] [1 1] [0 1] Get the first two rows of a_mat with: a_mat.matrix_from_rows(range(2)) [0 1 0 1] [1 1 1 1] Remove the first row from a_mat with: a_mat.delete_rows([0]) [1 1 1 1] [0 1 1 1] swap the first two rows of a_mat with: a_mat.swap_rows(0, 1) [1 1 1 1] [0 1 0 1] [0 1 1 1]