NumPy Arrays and Linear Algebra

<p>The answer that minimizes the square error. (A)</p> Signup and view all the answers

<p>The solution vector x of the equation Ax = b. (B)</p> Signup and view all the answers

<p>dot() (C)</p> Signup and view all the answers

<p>To return the inverse of a matrix. (B)</p> Signup and view all the answers

<p>eig() (D)</p> Signup and view all the answers

<p>The determinant of the matrix. (C)</p> Signup and view all the answers

<p>It will return the index of the maximum element in the array. (D)</p> Signup and view all the answers

<p>Both the view and original array are affected. (A)</p> Signup and view all the answers

<p>Check if the base attribute is None. (C)</p> Signup and view all the answers

<p>copy() (D)</p> Signup and view all the answers

<p>Using the copy method (C)</p> Signup and view all the answers

<p>The first row of the array M. (C)</p> Signup and view all the answers

<p>None. (B)</p> Signup and view all the answers

<p>Use v = M.copy() and then modify v. (C)</p> Signup and view all the answers

<p>They must be of the same shape or broadcastable. (A)</p> Signup and view all the answers

<p>An array that shares data with another array. (B)</p> Signup and view all the answers

<p>Universal functions (B)</p> Signup and view all the answers

<p>np.ceil (C)</p> Signup and view all the answers

<p>A function that acts on a single value (C)</p> Signup and view all the answers

<p>Computes the tangent of each element in radians (A)</p> Signup and view all the answers

<p>[2.71828183, 7.3890561, 20.08553692] (B)</p> Signup and view all the answers

<p>np.floor (B)</p> Signup and view all the answers

<p>[2.0, 3.0, 4.0] (D)</p> Signup and view all the answers

<p>np.sqrt (C)</p> Signup and view all the answers

Universal functions in NumPy operate element-wise on arrays, applying the same function to each element. They are essential for performing mathematical operations efficiently on entire arrays.

NumPy provides a wide variety of pre-defined universal functions, including trigonometric functions (cos, sin, tan), exponential functions (exp), logarithms (log), rounding functions (ceil, floor, round), and many more.

You can create your own universal functions in NumPy using the vectorize function. This allows you to apply any Python function to each element of a NumPy array.

The vectorize decorator in NumPy provides a convenient way to automatically convert a regular Python function into a universal function.

A NumPy array view is a reference to the original array's data but with a different shape or perspective. It often facilitates efficient manipulation of data with minimal memory overhead.

Boolean arrays in NumPy are arrays where each element is a Boolean value (True or False). They are fundamental for filtering and selecting elements in arrays based on conditions.

Array indexing in NumPy allows you to access specific elements or subsets of an array using various methods, including integer indexing, slicing, and fancy indexing.

NumPy's advanced array indexing features, such as fancy indexing, allow you to select specific elements or subsets of an array using arrays of indices or Boolean conditions.

A NumPy array method for calculating the sum of all elements within a specified dimension, or across the entire array if no dimension is provided.

A NumPy array method that returns the minimum value along a specific dimension or the minimum value across the entire array.

A NumPy array method that calculates the product of all elements within a specified dimension, or across the entire array if no dimension is provided.

A NumPy array method that returns the index of the maximum value along a specific dimension, or across the entire array if no dimension is provided.

A NumPy array method that returns the index of the minimum value along a specific dimension, or across the entire array if no dimension is provided.

A NumPy array method that sorts the elements of the array along the axis dimension specified, or the last dimension if none is provided.

A NumPy array method that returns the indices that would sort the elements along the specified axis dimension.

A NumPy submodule containing mathematical functions for performing linear algebra operations on matrices and vectors.

A NumPy function within the linalg module that solves a system of linear equations defined by a non-singular matrix A and a corresponding vector b. Returns the solution vector x that satisfies Ax=b.

A NumPy function within the linalg module that performs the singular value decomposition (SVD) on a matrix A. Returns a tuple containing the U, S, and V matrices of the decomposition.

Invertible matrices have a unique inverse, allowing you to solve linear equations with a single solution.

The 'lstsq' function finds the best fit solution for equations that don't have exact solutions, minimizing the error.

A view is a reference to an existing array's data, but with a different shape or perspective. Changes in the view affect the original data.

The 'base' attribute tells you if an array is original or a view. If 'base' is None, it's original.

Slicing an array creates a view, meaning changes in the slice affect the original array.

The 'reshape()' method and transpose operation create views, so changes in the new shape also affect the original data.

Copying an array view creates an independent array, preventing changes from affecting the original.

Comparison operations between arrays work element-wise, comparing corresponding entries. They also work on broadcastable arrays.

Arrays with different shapes can be compared if they are broadcastable - meaning their sizes are automatically adjusted.