Linear Algebra Fundamentals

%matplotlib inline import numpy as np import matplotlib.pyplot as plt scalar = True vector = np.array([1, 2, 3]) matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) #3x3 matrix #A tensor is a matrix of matrices: mario = np.array([ [[192,192,192],[128,128,128],[192,192,192],[128,128,128],[192,192,192],[232,12,12],[221,11,10],[210,0,0],[199,1,0],[200,0,0],[189,5,5],[128,128,128],[192,192,192],[128,128,128],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[128,128,128],[192,192,192],[221,11,10],[254,0,0],[245,0,10],[245,0,10],[234,0,9],[223,6,14],[223,6,14],[189,5,5],[200,0,2],[210,0,0],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[192,192,192],[128,128,128],[98,78,43],[106,82,46],[117,92,51],[197,177,144],[209,189,154],[204,184,149],[27,27,27],[197,177,144],[192,192,192],[128,128,128],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[128,128,128],[98,78,43],[213,194,162],[117,92,51],[213,194,162],[214,197,169],[218,199,167],[213,194,162],[47,47,47],[209,189,156],[204,184,149],[197,177,144],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[192,192,192],[92,68,30],[218,199,167],[128,100,60],[214,197,169],[218,199,167],[218,199,167],[213,194,162],[208,189,156],[27,27,27],[208,189,156],[203,183,150],[197,177,144],[128,128,128]], [[128,128,128],[192,192,192],[128,128,128],[78,57,26],[92,68,30],[197,177,144],[218,199,167],[213,194,162],[208,189,156],[208,189,156],[27,27,27],[47,47,47],[63,63,63],[27,27,27],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[192,192,192],[128,128,128],[192,192,192],[204,184,149],[213,194,162],[209,189,154],[204,184,149],[197,177,144],[204,184,149],[204,184,149],[197,177,144],[128,128,128],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[128,128,128],[192,192,192],[221,11,10],[210,0,1],[92,49,224],[200,0,0],[212,0,0],[221,11,10],[42,41,220],[192,192,192],[128,128,128],[192,192,192],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[192,192,192],[232,12,12],[254,0,0],[245,0,10],[84,45,214],[245,0,10],[234,0,9],[83,46,201],[210,0,1],[221,11,10],[232,12,12],[128,128,128],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[232,12,12],[254,0,0],[245,0,10],[234,0,9],[84,45,214],[92,49,224],[84,45,214],[77,41,189],[234,0,9],[245,0,10],[254,0,0],[221,11,10],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[197,177,144],[208,191,161],[245,0,10],[84,45,214],[247,223,61],[92,49,224],[83,46,201],[225,202,47],[67,35,172],[232,1,9],[208,191,161],[197,177,144],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[204,184,149],[214,197,169],[197,177,144],[84,45,214],[92,49,224],[84,45,214],[83,46,201],[77,41,189],[67,35,172],[197,177,144],[214,197,171],[204,184,149],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[209,189,154],[204,184,149],[84,45,214],[98,55,233],[92,49,224],[83,46,201],[77,41,189],[83,46,201],[77,41,189],[67,34,173],[204,184,149],[209,189,154],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[128,128,128],[192,192,192],[84,45,214],[84,45,214],[83,46,201],[192,192,192],[128,128,128],[67,35,172],[67,35,172],[67,35,172],[128,128,128],[192,192,192],[128,128,128],[192,192,192]], [[192,192,192],[128,128,128],[192,192,192],[107,83,45],[117,92,51],[111,86,45],[91,67,29],[128,128,128],[192,192,192],[102,78,40],[111,86,45],[103,80,38],[84,61,27],[128,128,128],[192,192,192],[128,128,128]], [[128,128,128],[192,192,192],[107,83,45],[102,78,40],[96,72,34],[91,67,29],[84,61,27],[192,192,192],[128,128,128],[96,72,34],[91,67,29],[84,61,27],[73,54,21],[65,48,18],[128,128,128],[192,192,192]] ]) #Tensors can describe images plt.imshow(mario, interpolation='nearest') plt.show()

scalar = 6.32 vector = np.array([1, 2, 3]) matrix = np.array([[1, 2, 3], [4, 5, 6]]) tensor = np.array([ [[1, 2, 3], [4, 5, 6], [7, 8, 9]], [[10, 11, 12], [13, 14, 15], [16, 17, 18]], [[19, 20, 21], [22, 23, 24], [25, 26, 27]] ])

print(len(vector)) print(len(matrix)) print(len(tensor))

print(vector.shape) print(matrix.shape) print(tensor.shape) #num of matrices, rows, columns

print(vector.size) print(matrix.size) print(tensor.size)

%matplotlib inline import numpy as np import matplotlib.pyplot as plt scalar = 6.32 vector = np.array([1, 2, 3]) matrix = np.array([[1