Turn matrix rules into pictureable geometry, from arrows and areas to invariant directions
5 sections · 7 lessons
Build the arrow picture for vectors, then examine a 2×2 matrix as a transformation of the unit square.
2 lessonsTrace transpose and matrix multiplication in geometric terms, then relate each algebraic move to what happens under the map.
2 lessonsExamine determinant as signed area scaling, including collapse to a line and orientation flip.
1 lessonUse precise terminology for basis, spanning set, rank, nullity, linear independence, and orthogonality.
1 lessonIdentify eigenvectors as directions left fixed by a transformation and close with the algebra to geometry dictionary.
1 lessonVectors in the plane become arrows first, not coordinate pairs, so matrix rules can be read as changes in shape, direction, and area. This course is for learners who can already compute with matrices but want the geometry behind the algebra, including linear maps, transpose, multiplication, determinant, terminology, and eigenvectors. By the end, matrix statements line up with geometric meaning instead of memorized symbols.
Vectors as arrows in the plane, matrices as linear maps, transpose as dual geometry, and matrix multiplication as composition. It also covers determinant as signed area scaling, precise vector-space terminology, and eigenvectors as invariant directions with an algebra to geometry dictionary.
From project managers and operators to founders, analysts, and teams adopting AI, Fenzo is for people who want to get better at the work they already do.
Anything from using AI for project planning and analysis to improving workflows, decision-making, communication, and delivery. If you can describe the skill or task, Fenzo can build a course around it.
Yes. Tell Fenzo what you do, what you’re trying to accomplish, and where you’re stuck, and Fenzo will shape the course around your role, your goals, and the work you actually have to do.
No. Fenzo adapts to your starting point, so you can begin with the fundamentals or jump straight into more advanced work.
Yes. Fenzo for Business puts the whole team on one plan — shared seats, courses you can assign, and reporting on who has finished what.
See Fenzo for BusinessYou start by describing your goal or taking a short skill benchmark. Fenzo uses that context to identify gaps and shape the learning experience around them.
Yes, Fenzo works in your mobile browser.
Something to operate in every section.
Three findings from decades of learning research shaped how every Fenzo lesson is built.
Average pass rate · Freeman et al., PNAS 2014
What the science says
Students in lecture-only classes are 1.5× more likely to fail.
How Fenzo does it
Every Fenzo lesson is interactive. No passive reading or watching, ever.
You work through itAI does it for you
Skill retention over time · with vs. without practice
What the science says
Offloading thinking to AI erodes the very skills you’re trying to build.
How Fenzo does it
Fenzo makes you do the thinking — guided, but never done for you.
Retrieval practiceRe-reading
Long-term recall · retrieval vs. re-reading
What the science says
Recalling information beats re-reading it for building durable understanding.
How Fenzo does it
Lessons weave in quizzes and recall prompts, so it sticks.