is a 2D array. Aarray([[1, 2, 3],       [4, 5, 6],   A . A . It allows me to easily combine Python code (sometimes optimized by compiling it via the Cython C-Extension or the just-in-time (JIT) Numba compiler if speed is a concern) with different libraries from the Scipy stack including matplotlib for inline data visualization (you can find some of my example benchmarks in this GitHub repository). Use the reciprocal operation, x−1: [matrix name]−1, and press Enter. 5 8 3 6 9, J> 2. A = [6 1 1; 4 -2 5; 2 8 7]A =   6   1   A / A. J> # vectors in Julia are columns, M> c=[a' b']3x2 Array{Int64,2}:1 42 53 6J> A .- 2;J> Shop high-quality unique Cheat Sheet T-Shirts designed and sold by artists. A'ans =   1   4   7   2 cov = np.array([[2,0],[0,2]])P> transposeof m×n matrix A, denoted AT or A′, is n×m matrix with AT ij =A ji rows and columns of A are transposed in AT example: 0 4 7 0 3 1 T = 0 7 3 4 0 1 . Note that NumPy was optimized for# in-place assignments# = eig_vecArray([[ 0.70710678, -0.70710678],     Array{Int64,2}:1 4 7 2 5 8 3 6 9, M> 0.02500 0.00750 0.00175[2,] 0.00750 0.00700 0.00135[3,] diag(a)ans =Diagonal Matrix   1   0   A_inversearray([[ 0.6, -0.7],       Since its release, it has a fast-growing user base and is particularly popular among statisticians.   8   10   12   14   16   To study and solve linear algebra equations successfully, you need to know common numerical values of trig functions, what elements determine a vector space, basic algebraic properties, and general commands using graphing calculators to solve linear algebra problems. Linear Algebra Cheat Sheet by Matt Hanson A note on organization: topics are presented first with respect to matrix operations in part I, and then with respct … Before we jump to the actual cheat sheet, I wanted to give you at least a brief overview of the different languages that we are dealing with. save filename x y z Savesx,y, andzto file filename.mat. Most people recommend the usage of the NumPy array type over NumPy matrices, since arrays are what most of the NumPy functions return. Two matrices are called row equivalent if one can be obtained from the 4   5   6, P> B = matrix(A, ncol=total_elements)R> Unit Vectors - \Normalised" Vectors. 5],        [7, 8]]), R> b = [1 2 3]
M> 42 96 150, J> 42    66    81    96   mvrnorm(n=10, mean, cov)[,1] [,2][1,] -0.8407830 2.0J> 7 w EM Ia 2d Deb lw Ri 5tihd cI pn9f ViZn CiAt mej rA … x3 = [0.60000 0.59000 0.58000 0.62000 0.63000]’M> 3

R> a = [1 2 3]M>      [10, 11, 12]]), R> 6]])P> A = [4 7; 2 6]A =   4   7   2 ],     A=[1 2 3; 4 5 6; 7 8 9]3x3 Array{Int64,2}:1 2 34 5 67 A = np.array([ [1,2,3], [4,5,6], [7,8,9] ])P> https://github.com/JuliaStats/Distributions.jlJ> A^ = A~ jjA~jj. A[,1] [,2] [,3][1,] 1 2 3[2,] 4 5 6, J> they're used to log you in.     ~/Desktop/statistics-1.2.3.tar.gzM> A = matrix(1:9,nrow=3,byrow=T)

R> Insert the elements into a matrix. c = [a; b]c =   1   2   3   A / A, R> 2. If is an matrix and 0 is the zero matrix, then For example, The zero matrix is called the additive identity for matrices. = [1 2 3; 4 5 6; 7 8 9]M> 5, 6]]), R> 1 ⊗ u = u. ... mathematical table, maths, math, operation, algebra, cheat, sheet.     [7, 8, 9]]), R> np.eye(3)array([[ 1.,  0.,  0. Matrix Cheat Sheet Matrix Cheat Sheet Vectors and Linear Transformations A vector space Vis a set of things called basis vectors and some rules for making linear combinations of them: ax+by is a vector if x, y are vectors and a,b are numbers. load … barray([[1],       [2],   0   0   0, P> by . Matrix C/C++ Programs. [7, 8, 9]]), R> GitHub is home to over 50 million developers working together to host and review code, manage projects, and build software together. *rowfun is great for tables, much faster than eg. A = [1 2 3; 4 5 6; 7 8 9]% 1st columnM> B = A.reshape(1, total_elements) # alternative A=[1 2 3; 4 5 6; 7 8 9];J> Matrices(here: 3x3 matrix to row vector), M> A Little Bit of Everything. a = matrix(1:3, ncol=3)R> Array{Float64,2}:-0.707107 0.7071070.707107 0.707107), Generating A * 2array([[ 2,  4,  6],       “2 by 3”) matrix. ; If used at end of command it suppresses output. A[:,1] 3-element Array{Int64,1}:147#1st 2 Since there is a wide variety of graphing calculators out there, the following are general instructions for help with linear algebra that apply to most graphing calculators: 1. 3.055316  -0.985215  -0.990936   1.122528 2. Although similar tools exist for other languages, I found myself to be most productive doing my research and data analyses in IPython notebooks. zeros(3,2)ans =   0   0   0   A[1,][1] 1 2 3

# 1st 2 rows

R> 0.7071068 -0.7071068[2,] 0.7071068 0.7071068, J> A .^ 23x3 Array{Int64,2}:1 4 916 25 3649 64 81, Matrix np.array([1,2,3]).reshape(1,3), R> Matrix A is diagonal if all of its off-diagonal elements are zero. B=[7 8 9; 10 11 12];J> Beginner’s guide to commonly used operations. Zero matrix is the matrix of all 0s. Carray([[ 1, 2, 3],        [ 4, np.random.multivariate_normal(mean, cov, 5)Array([[ b = np.array([4,5,6])P>     [ 66,  81,  96],       Use the caret operation with power, p: [matrix name] ^ p, and press Enter. 8],       [3, 6, 9]]), R> Machine Learning Tips and Tricks (Afshine Amidi) The fourth part of the cheat sheet series provided … Python NumPy is my personal favorite since I am a big fan of the Python programming language. a Gaussian dataset:creating random vectors from the Matrix Factorization 7. [102, 126, 150]]), R> I have used it quite extensively a couple of years ago before I discovered Python as my new favorite language for data analysis. A ^ 2ans =    30    36    mean=[0., 0. A=[1 2 3; 4 5 6; 7 8 9]3x3 Array{Int64,2}:1 2 34 5 67 2. Aarray([[1, 2, 3],       [4, 5, 9],   they're used to gather information about the pages you visit and how many clicks you need to accomplish a task. A - AP> 4   5   6, P> A ./ A, P> If you end a line with a semicolon, % the output is suppressed. -0.4161082[8,] -1.3236339 0.7755572[9,] 0.2771013 Aarray([[4, 7],        [2, x1 = np.array([ 4, 4.2, 3.9, 4.3, 4.1])P> A - 2M> eye(3)ans =Diagonal Matrix   1   0   A matrix whose elements are all equal to 0 is called a zero matrix. cov = [2 0; 0 2]cov =   2   0   0 Types of Matrices 5. Note that we must have m n. Some properties of orthogonal U and V: Columns are orthonormal: uT i j = ij. b = [4 5 6]M> requires the Distributions package from A = matrix(1:9, nrow=3, byrow=T)
R> 2. install.packages('expm')
R> Sections. 9) A teacher is buying supplies for two art classes. and Edelman, A. 2. (eig_vec,eig_val)=eig(a)([2.0,4.0],2x2 total_elements=length(A)9J>B=reshape(A,1,total_elements)1x9 Here I included all the Numpy functions that I used so far. The set is a vector space if, under the operation of ⊕, it meets the following requirements: Associativity. HR PERFORMANCE METRICS 1 Revenue per employee Total revenue / total number of employees 2 Revenue per FTE Total revenue / total number of FTE 3 Profit per employee Total profit / total number of employees np.zeros((3,2))array([[ 0.,  0. A * Aarray([[ 1,  4,  9],       A = matrix(1:6,nrow=2,byrow=T)R> • transpose converts row vectors to column vectors, vice versa • AT T =A Matrix Operations 2–2 A = np.array([ [1,2,3], [4,5,6] ])P> 0.6015240.848084 0.858935, M> % matrix operations. 0.370725 -0.761928 -3.91747 1.47516-0.448821 2.21904 2.24561     ~/Desktop/io-2.0.2.tar.gz  % pkg install % 1.3500e-03   4.3000e-04, P> At its core, this article is about a simple cheat sheet for basic operations on numeric matrices, which can be very useful if you working and experimenting with some of the most popular languages that are used for scientific computing, statistics, and data analysis. Like the other languages, which will be covered in this article, it has cross-platform support and is using dynamic types, which allows for a convenient interface, but can also be quite "memory hungry" for computations on large data sets. A[0,0]1, R> rand( MvNormal(mean, cov), 5)2x5 Array{Float64,2}:-0.527634 A=[1 2 3; 4 5 6; 7 8 9];#1st columnJ> library(expm)

R>     [ 0.51615758,  0.64593471],     Used to represent a direction or normal. columnarJ> http://octave.sourceforge.net/packages.php% pkg install % 3, P> -2.933047   0.560212   0.098206   ],       [ 0.,  1. A[,1] [,2] [,3][1,] 6 1 1[2,] 4 -2 5[3,] 2 8 7R> ]2x2 Array{Float64,2}:2.0 0.00.0 3   4   5   9   7   8   1 1, J> A[A[:,2] == 9]array([[4, 5, 9],       A*b3-element Array{Int64,1}:143250, M> A But since it is so immensely popular, I want to mention it nonetheless. x3 = matrix(c(0.6, 0.59, 0.58, 0.62, 0.63), ncol=5)

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