PPT-Unit 2: What is a matrix – really?

Sec 1 Organizing Data into Matrices Learning Target I will organize information using matrices give dimensions of a matrix and identify elements of a matrix Homework Organizing Data into Matrices Worksheet. Rev: . Nov, . 2012. Euiho. (David) . Suh. , Ph.D.. POSTECH Strategic Management of Information and Technology Laboratory. (POSMIT: http://posmit.postech.ac.kr). Dept. of Industrial & Management Engineering. Matrix Transformations. Dr J Frost (jfrost@tiffin.kingston.sch.uk). www.drfrostmaths.com . Last modified: . 3. rd. January 2016. The . specification:. Introduction. A matrix (plural: matrices) is . simply an ‘array’ of numbers. vectors and matrices. A vector is a bunch of numbers. A matrix is a bunch of vectors. A vector in space. In space, a vector can be shown as an arrow. starting point is the origin. ending point are the values of the vector. m. movies. v11. …. …. …. vij. …. vnm. V[. i,j. ] = user i’s rating of movie j. n . users. Recovering latent factors in a matrix. m. movies. n . users. m. movies. x1. y1. x2. y2. ... ... …. DETERMINANT. a “determinant” is a certain . kind of . function that associates a real number with a square . matrix. We will . obtain a formula for the inverse of an invertible matrix as well as . . Ossama. Inverse Matrix :. If . A. is a square matrix. , and if a . matrix . B. of the same size . can be found such that . AB = BA = I. , then . A. is said to be . invertible. and . B. is called an . m. columns. v11. …. …. …. vij. …. vnm. n . rows. 2. Recovering latent factors in a matrix. K * m. n * K. x1. y1. x2. y2. ... ... …. …. xn. yn. a1. a2. ... …. am. b1. b2. …. …. bm. v11. Solving triangular systems. Forward substitution - For solving Lower triangular systems. Consider a system described by the following equation . . . If then the unknowns can be determined sequentially. Lecture 4, Part B:. Orientation Representation. 1. Rotation Representation. 2. We saw that for computer graphics/games, the three most commonly used transforms are: . translation. , . rotation. . and . Biology 201 Organismal S&F. Dr. Tony Serino. Biology Department. Misericordia University. Skeletal System. Composed of mineralized CT and their supporting structures including: bone, cartilage, ligaments, tendons, and bursae. In 1928 Dirac proposed the following form for the electron wave equation:. The four . . µ . matrices form a Lorentz 4-vector, with . components, µ. That is, they transform like a 4-vector . under Lorentz transformations between moving . Inertial Measurement Unit (IMU) Basics IMU (Inertial Measurement Unit) Accelerometer Gyroscope Magnetometer (Compass) Acceleration along 3 axes Rotation speed around 3 axes Direction of magnetic north Approaches of BCG Matrix. Components of BCG Matrix. Applications of BCG Matrix. Advantages of BCG Matrix . Limitations of BCG Matrix . ?. The BCG Matrix . . .. High. Low. Relative position (Market Share). DEFINITION OF MATRIX. Matrices Definition. Matrices.  are the ordered rectangular array of numbers, which are used to express linear equations. A matrix has rows and columns. we can also perform the mathematical operations on matrices such as addition, subtraction, multiplication of matrix. Suppose the number of rows is m and columns is n, then the matrix is represented as m × n matrix..