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Everything about Transformation matrix

Central object in linear algebra; mapping vectors to vectors

In linear algebra, linear transformations can be represented by matrices. If is a linear transformation mapping to and is a column vector with entries, then there exists an matrix, called the transformation matrix of, such that: Note that has rows and columns, whereas the transformation is from to. There are alternative expressions of transformation matrices involving row vectors that are preferred by some authors. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Transformation matrixA 5-minute orientation
  2. Skim a recent paper: Matrix metalloproteinase‑9 in hemorrhagic transformation after acute ischemic stroke (Review)Influential work since 2022
  3. Pick up a classic book: Generalized inverses of linear transformationsThe most-reprinted book on the subject
  4. Read the landmark paper: Matrix Transformation between Some Classes of SequencesCited 54 times
  5. Go sideways: Rotation (mathematics)A closely related topic
  6. Go sideways: Affine transformationA closely related topic

📖 Definitions

Noun A matrix (of dimension n×m) that represents some linear transformation from ℝ→ℝ.

🗂️ The subject at a glance

  1. Uses
  2. Finding the matrix of a transformation
  3. Examples in 2 dimensions
  4. Examples in 3 dimensions
  5. Composing and inverting transformations
  6. Other kinds of transformations

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics