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  • Operations on matrices

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  • Addition
  • Conjugation
  • Scalar multiplication
  • Row operations
  • Matrix-vector products
  • Multiplication
  • Transpose and adjoint
  • Inverse

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  • Definition of left inverse of a matrix
  • Definition of right inverse of a matrix
  • Definition of inverse of a matrix
  • Definition of invertible matrix
  • If a matrix has both a left and a right inverse
  • If a square matrix has a one-sided inverse
  • Formula for the inverse of a 2-by-2 matrix.
  • Matrix inverse is an involution.
  • For n-by-n invertible matrices A and B
  • The product of square matrices is nonsingular if and only if each factor is nonsingular.
  • The inverse of a scalar multiple is the reciprocal times the inverse.
  • Matrix transpose commutes with matrix inverse.
  • The inverse of a matrix (if it exists) can be found by row reducing the matrix augmented by the identity matrix.
  • Example of finding the inverse of a 2-by-2 matrix by row reducing the augmented matrix
  • Example of finding the inverse of a 2-by-2 matrix by using a formula
  • Example of finding the inverse of a 3-by-3 matrix by row reducing the augmented matrix
  • Example of finding the inverse of a 3-by-3 matrix by using Cramer's rule
  • The inverse of a matrix can be used to solve a linear system.
  • Matrix inverses are unique: if A and B are square matrices
  • Definition of generalized inverse of a matrix
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701–715 of 715 nodes
  • Triangular matrices#23561
  • Two matrices of the same size are equivalent if and only if they have the same rank.#23607
  • Two vectors are orthogonal if and only if the Pythagorean Theorem holds.#23918
  • Unitary matrices#23587
  • Unitary matrices are invertible.#23589
  • Unitary matrices have orthogonal (orthonormal) rows/columns.#23590
  • Unitary matrices preserve inner products.#23591
  • Unitary matrices preserve orthogonal (orthonormal) bases.#23592
  • Using matrices to solve linear systems#23760
  • Vector space isomorphism is an equivalence relation.#24003
  • Vector spaces#23775
  • Vector spaces with the same dimension are isomprphic.#24005
  • Vector sum/addition interpreted geometrically in R^n (or C^n)#23797
  • Vector sum/addition is commutative and associative#23787
  • Visualise a linear transformation on R^2 by looking at the image of a region#23852
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