Transpose at switching the entries from rows to columns and columns to rows. Matrices and determinants the material in this chapter will be covered in your linear algebra class math 254 at mesa. Perform operations on matrices and use matrices in applications algebra creating equations a. Discrete mathematics and its applications chapter 2 notes 2.
Matrices, vectors and discrete maths print materials to assist with any prerequisite mathematics required in usq courses. Free discrete mathematics books download ebooks online. Model system defined by zeros and poles of discrete transfer function. One innovation uses several major threads to help weave core topics into a cohesive whole. We call the individual numbers entriesof the matrix and refer to them by their row and column numbers. I this is why bijections are also calledinvertible functions instructor. Matrices in discrete math mathematics stack exchange. Mathematics stack exchange is a question and answer site for people studying math at any level and professionals in related fields. Discrete mathematics i fall 2014 identity matrix the identity matrix is a n n square matrix where the main diagonal consist of all ones and zeros elsewhere. Matrices in discrete mathematics and its applications. Random matrices universality proof techniques random matrix models we will consider a number of random matrix models, which can be either discrete or continuous. Discrete mathematics overview conceptual categories, domains, and clusters number and quantity vector and matrix quantities c.
In many economic analysis, variables are assumed to be related by sets of linear equations. This book is designed for a one semester course in discrete mathematics for sophomore or junior level students. Browse other questions tagged matrices discretemathematics graphtheory or ask your own question. Matrices in discrete mathematics and its applications slideshare. Here is a matrix of size 2 3 2 by 3, because it has 2 rows and 3 columns. Perform discretetime integration or accumulation of signal. You have probably encountered them in a precalculus course. Matrices a matrix is basically an organized box or array of numbers or other expressions. Prior to his 20year service at depaul university, he was a member and sometime chair of the mathematics departments at morehouse college and chicago state university. Definition of matrix a matrix is a rectangular array of numbers.
Matrix math equal matrices same order and each entry is equal question 16. From a night class at fordham university, nyc, fall, 2008. Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. We will usually denote matrices with capital letters, like.
In this video we guide you through matrix addition and subtraction. Discrete math functions perform operations on integers, 2, 1, 0, 1, 2, or return discrete output as integers. Definition of matrix square matrix with example matrix operations matrix multiplication with example transposes and power matrices. Matrices in discrete mathematics and its applications 1. In contrast to real numbers that have the property of varying smoothly, the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values.
Computer science stack exchange is a question and answer site for students, researchers and practitioners of computer science. This informative chapter offers a handy way to brush up on or learn something new about matrices in discrete math. Notes on matrices matrices is the plural of matrix a matrix is a rectangular array of data. This page intentionally left blank university of belgrade. Iid random matrices these are n n matrices a xij1 i. The aim of this book is not to cover discrete mathematics in depth it should be clear from the description above that such a task would be illde. A diagonal matrix is a square matrix whose entries o the main diagonal are zero. In the last lecture we introduced fast matrix multiplication, i. Throughout the book the application of mathematical reasoning is emphasized to solve problems while the authors guide the student in thinking about, reading, and writing proofs in a. These active and wellknown authors have come together to create a fresh, innovative, and timely approach to discrete math.
At uga, our linear algebra class focuses on the geometric interpretations of vectors and matrices, while the discrete course focuses on things like logic, complexity, graph theory, and cryptography. Matrix algebra provides a clear and concise notation for the formulation and solution of such problems, many of which would be complicated in conventional algebraic notation. View notes discrete math lecture notes matrices from 1016 265 at rochester institute of technology. Discrete was definitely easier, but they are so different that theres not enough overlap to. This booklet consists of problem sets for a typical undergraduate discrete mathematics course aimed at computer science students. Inverse functions i every bijection from set a to set b also has aninverse function i the inverse of bijection f, written f 1, is the function that assigns to b 2 b a unique element a 2 a such that fa b i observe. Among the fields covered by discrete mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic. Mathematical logic, set theory, the real numbers, induction and recursion, summation notation, asymptotic notation, number theory, relations, graphs, counting, linear algebra, finite fields. If the product, sum, andor difference does not exist, state why it. To add or subtract two matrices of the same dimensions, we add or subtract the corresponding entries. The rows in a matrix are usually indexed 1 to m from top.
Find each product, sum, andor difference, if possible, using the matrices below. Discrete mathematics for computer science i university of. Discrete math cheat sheetstudy sheetstudy guide in pdf. These problem may be used to supplement those in the course textbook. However, the rigorous treatment of sets happened only in the 19th century due to the german mathematician georg cantor. Among the fields covered by discrete mathematics are graph and hypergraph theory, network theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Johnsonbaugh, discrete mathematics, 8th edition pearson. Browse other questions tagged discretemathematics matrices or. Number theory, probability, algorithms, and other stuff by j. A matrix with m rows and n columns is called an m xn matrix. The text covers the mathematical concepts that students will encounter in many disciplines such as computer science, engineering, business, and the sciences. Cheat sheetstudy sheet for a discrete math class that covers sequences, recursive formulas, summation, logic, sets, power sets, functions, combinatorics, arrays and matrices. A square matrix is a matrix with the same number of rows as columns. Sets, set operations, cardinality of sets, matrices.
In general, an m n matrix has m rows and n columns and has mn entries. Click here to download the full size worksheet pdf. Discrete mathematics and probability algebra 2 mathplanet. The numbers n and m are called the dimensions of the matrix. He was solely responsible in ensuring that sets had a home in mathematics. Matrices are used throughout discrete mathematics to express relationships between elements. Suppose a fstudents in this math 42 class g and b fountriesc in the world other than the us g. Discrete mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics.
These materials are based on usqs tertiary preparation program. An upper triangular matrix is a matrix having all the entries below the main diagonal equal to zero. A matrix with m rows and n columns is called an m n matrix. Discrete here is used as the opposite of continuous.
This is a course note on discrete mathematics as used in computer science. Discrete mathematics matrix additionsubtraction youtube. A matrix with m rows and n columns is called an m x n matrix. The learner will use matrices and graphs to model relation ships and solve problems. Discrete mathematics and algorithms lecture 9 matrix. In this video we guide you through matrix order, which is a fancy way of saying matrix rows and columns click here to download the full size worksheet pdf. You can use these functions to factor large numbers, calculate factorials, find permutations and combinations, or find greatest common denominators. P kubelka equivalence relations a type of relation on athat is very important in many branches of mathematics is an equivalence relation. Among the fields covered by discrete mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and.
Cantor developed the concept of the set during his study of the trigonometric series, which is now known as the limit point or the derived set operator. Matrices have many applications in discrete mathematics. Besides reading the book, students are strongly encouraged to do all the. We continue our investigation of discrete riemann surfaces with the discussion of the discrete analogs of period matrices, riemanns bilinear relations, exponential of constant argument, series and electrical moves. Example here is a matrix of size 2 2 an order 2 square matrix.