Systems and matrices
- Row reduction and echelon forms
- Matrix operations and inverses
- Determinants
- LU factorization
Linear algebra · University
Linear algebra tutoring that makes the abstraction click.
Linear algebra is often the first university course where calculation is not enough. Krsna Academy tutors connect the matrix arithmetic to the geometry and the proofs, so the definitions start to mean something.
Linear algebra topics we tutor
First and second-year linear algebra for mathematics, engineering, computer science, physics, and economics students.
Vector spaces
- Span and linear independence
- Basis and dimension
- Subspaces, null space, and column space
- Rank and nullity
Transformations and eigen-theory
- Linear transformations
- Eigenvalues and eigenvectors
- Diagonalization
- Change of basis
Orthogonality and applications
- Inner products and projections
- Gram-Schmidt process
- Least squares
- Symmetric matrices and quadratic forms
Where linear algebra students most often get stuck
Definitions that feel abstract
Span, basis, and subspace make sense once you can picture them. We work in two and three dimensions first, then generalize.
Writing proofs
Many students have never been asked to prove something. We teach how to start from the definition and write an argument a marker can follow.
Seeing one idea in many forms
Invertibility, rank, determinant, and independence are the same story told differently. We make those connections explicit.
How it works
One-to-one tutorials, online or in person.
Every tutorial is 60 minutes with one tutor and one learner. Use the interactive tuition estimate to explore a plan around the learner's level, programme, delivery, and continuity needs.
Explore a tutoring plan01
Tell us about the learner
Grade, curriculum, subject, and what is most pressing right now. The consultation is free and takes 30 minutes.
02
Meet a tutor matched to the work
We recommend a tutor with the right subject depth and a way of explaining that suits the learner.
03
Follow a visible plan
After each tutorial the learner has clear next steps, and parents can see what was covered and what is improving.
Questions, answered
The questions we hear most.
Is this for a specific university's course?
We work from your course outline, whichever institution you attend. Send the course code and textbook when you book.
Do you tutor linear algebra for machine learning or data science?
Yes. We cover the matrix and vector ideas those fields rely on, including projections, least squares, and eigen-decomposition.
Start with a free consultation.
Tell us the course, the learner, and what would make the biggest difference. We will recommend a tutor and a plan.