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Merge pull request #3050 from madeline-underwood/eigen
Update Eigen documentation for consistency and clarity in headings
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content/learning-paths/cross-platform/eigen-linear-algebra-on-arm/_index.md

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title: Use the Eigen Linear Algebra Library on Arm
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description: Learn how to use the Eigen linear algebra library on Arm systems with ASIMD and SVE vectorization, including building TensorFlow with SVE support for optimized performance.
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minutes_to_complete: 45
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who_is_this_for: This is an advanced topic for C/C++ developers who want to create high performance applications using the Eigen linear algebra library.

content/learning-paths/cross-platform/eigen-linear-algebra-on-arm/eigen-intro.md

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In this Learning Path, you will test Eigen using a few examples with emphasis on Arm CPUs. For full documentation and a list of all supported types and operations on them, see the [Eigen documentation](https://libeigen.gitlab.io/docs/).
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## Numerical Solvers
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## Numerical solvers
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Besides basic vector and matrix types, Eigen also provides built-in methods for numerical solving on the matrices.
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content/learning-paths/cross-platform/eigen-linear-algebra-on-arm/eigen-on-arm-part1.md

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You have learned that Eigen has been ported to Neon/ASIMD in the past and recently to SVE. Now you are going to investigate how to use Eigen to get best performance on Arm systems with SIMD engines.
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## Example 1: Arbitrary-Size Matrix Sum of all Elements
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## Example 1: arbitrary-size matrix sum of all elements
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This example demonstrates the benefits of Eigen's vectorization with some simple expressions on matrices. It first constructs a large random matrix of 100 x 100 `float` elements, and performs some simple operation for `N` iterations on it. Finally, it returns the sum of all the elements of the final matrix as a `double`.
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content/learning-paths/cross-platform/eigen-linear-algebra-on-arm/eigen-on-arm-part2.md

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## Example 2: Matrix Multiplication
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## Example 2: matrix multiplication
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Use a text editor to save the program below in a file named `eigen-test3.cpp`:
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The SVE implementation is still experimental and performance is expected to improve in the future.
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## Example 3: Vector 3D Rotation
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## Example 3: vector 3D rotation
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This example creates an initial random normalized vector `v1`.
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