important concepts in this sectionwe discuss some key terms and concepts from applied mathematicsnamely linear algebra and probability theory these concepts are widely used across machine learning and form some of the foundational structures and principles across machine learning algorithmsmodelsand processes scalar scalar usually denotes single number as opposed to collection of numbers simple example might be or rwhere is the scalar element pointing to single number or real-valued single number vector vector is defined as structure that holds an array of numbers which are arranged in order this basically means the order or sequence of numbers in the collection is important vectors can be mathematically denoted as [ xn]which basically tells us that is one-dimensional vector having elements in the array each element can be referred to using an array index determining its position in the vector the following snippet shows us how we can represent simple vectors in python in [ ] [ out[ ][ in [ ]import numpy as np np array([ ]print(xprint(type( )[ thus you can see that python lists as well as numpy based arrays can be used to represent vectors each row in dataset can act as one-dimensional vector of attributeswhich can serve as inputs to learning algorithms matrix matrix is two-dimensional structure that basically holds numbers it' also often referred to as array each element can be referred to using row and column index as compared to single vector index in case em of vectors mathematicallyyou can depict matrix as em such that is matrix eem uu having three rows and three columns and each element is denoted by mrc such that denotes the row index and denotes the column index matrices can be easily represented as list of lists in python and we can leverage the numpy array structure as depicted in the following snippet in [ ] np array([[ ][ ][ ]]