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The following plot shows 5 vectors a₁, ..., a5: az -8 -6 аз + a4 80 9 4 P N e -2 -2 -4 6 % 2 a5 60 + 8 1. Define the numpy array a as the matrix whose columns are these 5 vectors. 2. Define a second array a_rot whose columns are the vectors a½ obtained by rotatating a (anticlockwise) by 115°. 3. Set up the matrix B whose entries Bij are the angles in degrees between a; and a'; (i.e., one original and one rotated vector). Assign the matrix (as a numpy array) to the variable B. (Hint: Recall that (u, v) = ||u||||v|| cos a, where a is the angle between u and v.)

The following plot shows 5 vectors a₁, ..., a5: az -8 -6 аз + a4 80 9 4 P N e -2 -2 -4 6 % 2 a5 60 + 8 1. Define the numpy array a as the matrix whose columns are these 5 vectors. 2. Define a second array a_rot whose columns are the vectors a½ obtained by rotatating a (anticlockwise) by 115°. 3. Set up the matrix B whose entries Bij are the angles in degrees between a; and a'; (i.e., one original and one rotated vector). Assign the matrix (as a numpy array) to the variable B. (Hint: Recall that (u, v) = ||u||||v|| cos a, where a is the angle between u and v.)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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The following plot shows 5 vectors a₁, ..., a5: az -8 -6 аз + a4 80 9 4 P N e -2 -2 -4 6 % 2 a5 60 + 8 1. Define the numpy array a as the matrix whose columns are these 5 vectors. 2. Define a second array a_rot whose columns are the vectors a½ obtained by rotatating a (anticlockwise) by 115°. 3. Set up the matrix B whose entries Bij are the angles in degrees between a; and a'; (i.e., one original and one rotated vector). Assign the matrix (as a numpy array) to the variable B. (Hint: Recall that (u, v) = ||u||||v|| cos a, where a is the angle between u and v.)
Transcribed Image Text:The following plot shows 5 vectors a₁, ..., a5: az -8 -6 аз + a4 80 9 4 P N e -2 -2 -4 6 % 2 a5 60 + 8 1. Define the numpy array a as the matrix whose columns are these 5 vectors. 2. Define a second array a_rot whose columns are the vectors a½ obtained by rotatating a (anticlockwise) by 115°. 3. Set up the matrix B whose entries Bij are the angles in degrees between a; and a'; (i.e., one original and one rotated vector). Assign the matrix (as a numpy array) to the variable B. (Hint: Recall that (u, v) = ||u||||v|| cos a, where a is the angle between u and v.)
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