Tutorial Lesson: Vector Algebra (Algebra with many numbers, all at once...)
Launch MATLAB and reproduce the following information. You type only what you see right after the '>>' sign. MATLAB confirms what you enter, or gives an answer. Let x be a row vector with 3 elements (spaces determine different columns). Start your vectors with '[' and end them with ']'. >> x=[3 4 5] x = 3 4 5 Let y be a column vector with 3 elements (use the ';' sign to separate each row). MATLAB confirms this column vector. >> y=[3; 4; 5] y = 3 4 5 You can add or subtract vectors of the same size: >> x+x ans = 6 8 10 >> y+y ans = 6 8 10 You cannot add/subtract a row to/from a column (Matlab indicates the error). For example: >> x+y ??? Error using ==> plus Matrix dimensions must agree. You can multiply or divide element-by-element of same-sized vectors (using the '.*' or './' operators) and assign the result to a different variable vector: >> x.*x ans = 9 16 25 >> y./y ans = 1 1 1 >> a=[1 2 3].*x a = 3 8 15 >> b=x./[7 6 5] b = 0.4286 0.6667 1.0000 Multiplying (or dividing) a vector with (or by) a scalar does not need any special operator (you can use just '*' or '/'): >> c = 3*x c = 9 12 15 >> d = y/2 d = 1.5000 2.0000 2.5000 The instruction 'linspace' creates a vector with some elements linearly spaced between your initial and final specified numbers, for example: r = linspace(initial_number, final_number, number_of_elements) >> r = linspace(2,6,5) r = 2 3 4 5 6 or >> r = linspace(2,3,4) r = 2.0000 2.3333 2.6667 3.0000 Trigonometric functions (sin, cos, tan...) and math functions (sqrt, log, exp...) operate on vectors element-by-element (angles are in radians). >> sqrt(r) ans = 1.4142 1.5275 1.6330 1.7321 >> cos(r) ans = -0.4161 -0.6908 -0.8893 -0.9900 Well done! So far, so good? Experimenting with numbers, vectors and matrices is good for you and it does not hurt! Vector algebra can even be fun if you work with a computer and a good software, can't it? Go on! From 'Vector Algebra' to home From 'Vector Algebra' to Tutorials
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