Linear Algebra

Study of vectors, matrices, and linear transformations.

Vectors and Their OperationsMatrices and Matrix ArithmeticLinear Transformations
Determinants and InversesEigenvalues and EigenvectorsVector Spaces and Subspaces
Computer Graphics and AnimationData Science and Machine LearningRobotics and Engineering
Breaking Down Word ProblemsChecking Your Solutions with InversesVisualizing Problems to Find Solutions
Vectors and Their Op...Matrices and Matrix ...Linear Transformatio...Determinants and Inv...Eigenvalues and Eige...Vector Spaces and Su...Computer Graphics an...Data Science and Mac...Robotics and Enginee...Breaking Down Word P...Checking Your Soluti...Visualizing Problems...
Practical Applications

Computer Graphics and Animation

Bringing Art to Life

In computer graphics, every image is made up of points (pixels) with coordinates. Matrices and vectors are used to move, rotate, scale, and animate these points.

  • Transforming Characters: Matrices help animate characters by rotating or moving their limbs.
  • Rendering Scenes: Linear algebra is key in producing realistic 3D graphics, from video games to animated movies.

Cool Fact

Every time you watch an animated film or play a video game, you're seeing linear algebra in action!

Practice

  • Move a 3D object by multiplying its coordinates with a translation matrix.
  • Rotate a sprite in a 2D game using a rotation matrix.

Examples

  • Rotating a 3D model in a game uses matrix multiplication.

  • Scaling an image up or down uses linear transformations.

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Data Science and Machine Learning