Linear Algebra Professional Certification
Vectors, matrices and transformations — the mathematics behind data science, graphics and machine learning
Key facts
- Level: Professional
- Field: Mathematics
- Estimated study time: about 32 hours
- Credential price: $149
- Exam: 88 questions · 140 minutes · pass mark 75%
About the Linear Algebra Professional certification
The Linear Algebra Professional certification proves you can reason fluently about vectors, matrices and linear transformations — the mathematical engine beneath machine learning, computer graphics, data science, engineering, quantum mechanics and optimisation. You will master vectors and vector spaces (vector operations, the dot and cross products, norms and distance, linear combinations and span, subspaces and the axioms of a vector space); systems of linear equations (Gaussian elimination, reduced row-echelon form, rank, and the consistency conditions that decide whether a system has no, one, or infinitely many solutions); the full algebra of matrices (multiplication, transpose, inverse, and the special matrices — identity, diagonal, symmetric, orthogonal, triangular); determinants (cofactor expansion, the product and row-operation properties, and Cramer's rule); linear independence, basis and dimension, and the four fundamental subspaces (column space, null space, row space and left null space) tied together by the rank-nullity theorem; linear transformations (their matrix representation, kernel and image); eigenvalues and eigenvectors (the characteristic polynomial, diagonalisation and similarity); orthogonality (projections, the Gram-Schmidt process and orthogonal matrices); inner product spaces, the spectral theorem, and symmetric and positive-definite matrices; an introduction to the singular value decomposition (SVD); and the applications that make all of this matter — least squares, principal component analysis (PCA), Markov matrices and graphics transforms. Every topic is taught and tested with worked, numerical examples — you finish able to row-reduce a system by hand, compute an inverse or a determinant, find eigenvalues and eigenvectors, project a vector and run Gram-Schmidt, and read the geometry behind every computation. It builds on algebra and pre-calculus and is the natural foundation for data science, machine learning and advanced engineering credentials.
What you will learn
The official Linear Algebra Professional study course covers:
- Vectors & Vector Spaces — Vector operations, dot and cross products, norms, linear combinations, span and subspaces.
- Systems & Gaussian Elimination — Solving linear systems, row reduction to RREF, rank, and the consistency conditions.
- Matrices & Determinants — Matrix algebra, transpose and inverse, special matrices, and the determinant with its properties.
- Independence, Basis & the Four Subspaces — Linear independence, basis and dimension, and the four fundamental subspaces with rank-nullity.
- Transformations & Eigenvalues — Linear transformations and their matrices, kernel and image, eigenvalues, eigenvectors and diagonalisation.
- Orthogonality, Spectral Theorem & SVD — Projections, Gram-Schmidt, orthogonal matrices, the spectral theorem, SVD and real applications.
Prerequisites
Frequently asked questions
- Is the Linear Algebra Professional certificate verifiable?
- Yes. Every issued Hootix Academy certificate carries a unique credential code that anyone can verify online.
- How is the Linear Algebra Professional exam structured?
- It is a 140-minute proctored multiple-choice exam of 88 questions; you need 75% to pass.
- Do I need to buy the course to take the exam?
- You can purchase the certification exam on its own, or bundle it with the full study course at a reduced price.
- How long does the Linear Algebra Professional course take?
- About 32 hours of self-paced study.