## Laura Lyman

PhD student
Stanford University, ICME |

Laura Lyman is a PhD candidate at Stanford University in the Institute for Computational and Mathematical Engineering (ICME). She researches theoretical and numerical aspects of polynomial chaos methods, with Professor Gianluca Iaccarino as her advisor. Broadly, Laura is fascinated by how we account for uncertainty when modeling natural phenomena.
Laura has lectured previously for Stanford's computational linear algebra course CME 200 in 2017, 2018, and 2020. She has mentored in STEM through a variety of programs, such as: Data Days 2021, Stanford Women Mentoring in Mathematics (SWIMM), and the Stanford Math Directed Reading Program (DRP). More recently, Laura has co-taught a course on algorithms to high school girls through Stanford's SPLASH program. |

**Workshop:**

**What would we do without Linear Algebra, part III: Singular Value Decomposition and Principal Component Analysis**

**September 29, 2021; 8:00-9:15 am PST**

In this third workshop in linear algebra, we will investigate the link between Principal Component Analysis and the Singular Value Decomposition.

Along the way, we are introduced to several linear algebra concepts including linear regression, eigenvalues and eigenvectors and conditioning of a system. We will use shared python scripts and several examples to demonstrate

the ideas discussed.

This workshop builds on the previous 2 workshops in linear algebra (Part I and Part II), and we will assume that the linear algebra concepts introduced in those workshops are familiar to the audience. They include: vector algebra (including inner products, angle between vectors), matrix-vector multiplications, matrix-matrix multiplications, matrix-vectors solves, singularity, and singular values.

Along the way, we are introduced to several linear algebra concepts including linear regression, eigenvalues and eigenvectors and conditioning of a system. We will use shared python scripts and several examples to demonstrate

the ideas discussed.

This workshop builds on the previous 2 workshops in linear algebra (Part I and Part II), and we will assume that the linear algebra concepts introduced in those workshops are familiar to the audience. They include: vector algebra (including inner products, angle between vectors), matrix-vector multiplications, matrix-matrix multiplications, matrix-vectors solves, singularity, and singular values.

**Workshop:**

**What would we do without Linear Algebra, part II: Diving Deeper into the Singular Value Decomposition**

**May 26, 2021; 8:00-9:15 am PST**

**Prerequisite**

**:**We will assume that you are familiar with the vector and matrix algebra discussed in part I (see below).

This is the second of our workshops devoted to linear algebra, which forms the foundation of many algorithms in data science. In part I of the series we introduced vector and matrix algebra, and briefly looked at the intriguing and ever so useful Singular Value Decomposition (SVD). In this workshop, we will take a deeper into the SVD. We will explain how it is derived, how it can be computed, and also how it is used.

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