IA ideas library
Matrix IA ideas: transformations, Markov chains and long-term behaviour
Matrices turn a system with many parts into one object you can calculate with. A transition matrix predicts where things end up, a transformation matrix moves an image, and powers and eigenvalues describe what happens in the long run.
Matrices, transformations, Markov chains and eigenvalues are in AI HL. AA students can still use them if they explain them as new mathematics, and a small system worked by hand goes a long way before you hand the calculation to technology.
Matrices, transformations & Markov chains ideas (8)
- Does rain today predict rain tomorrow? A Markov chain for the weatherAI HLAA HLSolid
- Animating a logo with transformation matricesAI HLAA HLSolid
- Projecting a country's age structure with a Leslie matrixAI HLAmbitious
- Can letter transitions tell languages apart? Markov chains for textAI HLAA HLAI SLSolid
- Gambler's ruin: how long until someone runs out?AI HLAA HLAmbitious
- How does a game draw 3D on a flat screen? Projection matricesAI HLAA HLAmbitious
- Balancing traffic flow through a road network with linear equationsAI HLAI SLAA HLSolid
- Ranking teams that haven't all played each other: the Colley matrixAI HLAA HLAmbitious
Also relevant (5)
- How does Google rank pages? PageRank on a small websiteAI HLAA HLAmbitious
- Will one phone brand take over? Brand loyalty as a Markov chainAI HLSolid
- How long does a game of Snakes and Ladders last?AI HLAA HLAmbitious
- Which Monopoly squares are landed on most often?AI HLAA HLAmbitious
- Encrypting with matrices: when can a Hill cipher be undone?AI HLAA HLAmbitious
Frequently asked questions
Are Markov chain IAs only for AI HL?
Markov chains are examined in AI HL, but any student can use them if they explain transition matrices and matrix multiplication clearly. AA students should add mathematics of their own course, such as a proof or a limit.
Where do I get a transition matrix from?
From data you count yourself (weather records, a game, people's choices) or from a published dataset. Show how each probability was estimated and how many observations it came from.
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