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Everything about Diagonal matrix

Matrix whose only nonzero elements are on its main diagonal

In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is, while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it is a diagonal matrix called a scalar matrix, for example,. In geometry, a diagonal matrix may be used as a scaling matrix, since matrix multiplication with it results in changing scale (size) and possibly also shape; only a scalar matrix results in uniform change in scale. Wikipedia →

🧭 Start here: a 6-step reading path

  1. Read the overview: Diagonal matrixA 5-minute orientation
  2. Skim a recent paper: Robust adaptive beamforming via covariance matrix reconstruction with diagonal loading on interference sources covariance matrixInfluential work since 2022
  3. Pick up a classic book: Dot JournalThe most-reprinted book on the subject
  4. Read the landmark paper: An estimator for the diagonal of a matrixCited 147 times
  5. Go sideways: Eigenvalues and eigenvectorsA closely related topic
  6. Go sideways: Eigendecomposition of a matrixA closely related topic

📖 Definitions

Noun A matrix in which the entries outside the main diagonal are all zero.

🗂️ The subject at a glance

  1. Definition
  2. Vector-to-matrix diag operator
  3. Matrix-to-vector diag operator
  4. Scalar matrix
  5. Vector operations
  6. Matrix operations
  7. Operator matrix in eigenbasis
  8. Properties
  9. Applications
  10. Operator theory

🏆 Landmark papers (most cited)

🆕 Influential since 2022

📚 Books worth reading

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