Is Linear Algebra A Hard Class In College? - Salarship

In my experience, linear algebra is one of the most complex maths courses you can take as a freshman due to its abstract concepts.

Linear algebra requires excellent analytic skills and logical reasoning; some students find it even more challenging than calculus.

Let’s discuss how hard linear algebra is by going over the challenges.

Tip: Find College Student Jobs on Salarship.

3 Reasons Why Linear Algebra is Considered One of The Most Challenging Math Courses

There are the 3 main reasons why linear algebra is perceived as one of the most challenging courses:

1. High Exam Failure Rates

It is not uncommon for linear algebra exams to have high failure rates.

A report published in the European Journal of Engineering Education indicates that, on average, 51% of first-year students fail their linear algebra exams!

An engineering student even commented on Reddit that they had an 83% failure rate.

Unfortunately, these horror stories are often heard in engineering departments as linear algebra is used in the first year to “weed out” students.

2. Abstract Concepts Are Rarely Taught With Examples That Students Can Relate With

Let’s face it; college professors are not the best teachers.

Instead of using examples and concrete applications to teach linear algebra, college professors usually opt for an abstract approach with definitions, theorems, and lemmas.

This makes the subject challenging for students who do not have incredible analytical skills.

3. Rigorous Proof-Based Approach

Linear algebra is often the first college course students encounter taught using a rigorous, proof-based approach.

Students need to understand and construct mathematical proofs to validate theorems and concepts.

This demands a higher level of abstract thinking and logical reasoning, which can be challenging for students who are more accustomed to computation and calculation.

Transitioning from a computational mindset to a more theoretical one can be difficult.

Challenging Linear Algebra Topics

Here are challenging topics that make it difficult for students to understand linear.

• Eigenvalues and Eigenvectors — Understanding eigenvalues and eigenvectors involves grasping the concept of how a linear transformation scales and rotates vectors in a vector space. Finding eigenvalues (solving characteristic polynomials) can be algebraically intensive, especially for larger matrices.
• Singular Value Decomposition (SVD) — SVD is a generalization of the eigenvalue decomposition and involves decomposing a matrix into three other matrices, which reveal important properties about the original matrix. The complexity lies in the computation and understanding of the singular values and the role of orthogonal matrices in this decomposition.
• Advanced Matrix Decompositions (e.g., QR Decomposition, LU Decomposition, Schur Decomposition) — Advanced matrix decompositions are used in various applications, including numerical solutions to linear systems and optimization problems. Each decomposition method has specific conditions and implications, and understanding when and how to apply them correctly requires a deep understanding of both the algebraic and geometric properties of matrices.

The Bottom Line

Despite its inherent complexity, understanding linear algebra is essential for engineers.

Linear algebra is a prerequisite for many courses and for career paths in computer science, engineering, and mathematics.

Typically, one would find that any STEM (science, technology, engineering, and mathematics) student would be taking linear algebra.

Similar Articles

• Contemporary Math: An Easier Way to Approach Linear Algebra Concepts for Non-STEM Students
• How is Discrete Mathematics in College?
• How Often Do College Students Fail Statistics Exams?