Matrix analysis

In mathematics, particularly in linear algebra and applications, matrix analysis is the study of matrices and their abstract algebraic properties. Some particular topics out of many include; operations defined on matrices (such as matrix addition, matrix multiplication and operations derived from these), functions of matrices (such as matrix exponentiation and matrix logarithm, and even sines and cosines etc. of matrices), and the eigenvalues of matrices (eigendecomposition of a matrix, eigenvalue perturbation theory).

See also

• Mathematical analysis
• Tensor analysis
• Matrix calculus
• Numerical analysis
• Determinant
• Matrix norm
• Matrix similarity
• Tensor product
• Spectrum of an operator
• Positive definite matrix
• Unitary matrix
• Stochastic matrix

References

• R. A. Horn, C. R. Johnson (2012). Matrix Analysis (2nd ed.). Cambridge University Press. ISBN 052-183-940-8.

• C. Meyer (2000). Matrix Analysis and Applied Linear Algebra Book and Solutions Manual. Matrix Analysis and Applied Linear Algebra. Vol. 2. SIAM. ISBN 089-871-454-0.

• T. S. Shores (2007). Applied Linear Algebra and Matrix Analysis. Undergraduate Texts in Mathematics. Springer. ISBN 038-733-195-6.

• Rajendra Bhatia (1997). Matrix Analysis. Matrix Analysis Series. Vol. 169. Springer. ISBN 038-794-846-5.

• Alan J. Laub (2012). Computational Matrix Analysis. Undergraduate Texts in Mathematics. SIAM. ISBN 161-197-221-3.