ਮਾਤਰੀਕਸ

ਇੱਕ ਮਾਤਰੀਕਸ ਵਿੱਚ ਨੰਬਰਾ ਨੂੰ ਰਕਤਾਨਗੂਲਾਰ ਤਰਤੀਬ ਵਿਚ ਦਰਸਾਇਆ ਜਾਂਦਾ ਹੈ।

ਹਿਸਾਬ ਵਿੱਚ ਚਿੰਨ੍ਹ, ਨੰਬਰਾ ਜਾਂ ਅਲੀਮੈਨਤਾਂ ਦੀ ਰਕਤਾਨਗੂਲਾਰ ਤਰਤੀਬ ਨੂੰ ਮਾਤਰੀਕਸ ਕਹਿੰਦੇ ਹਨ । ਮਾਤਰੀਕਸ ਨੂੰ ਅਲਜਬਰਾ ਵਿੱਚ ਖ਼ਾਸ ਅਤੇ ਮੁਸ਼ਕਲ ਬਦਲਾਵਾਂ ਨੂੰ ਸੌਖੇ ਤਰੀਕੇ ਨਾਲ ਦਰਸਾਉਣ ਲਈ ਵਰਤਿਆ ਜਾਂਦਾ ਹੈ ।

ਪਿਛੋਕੜ

ਸਭ ਤੋਂ ਪਹਿਲਾਂ ਇਹਨਾਂ ਨੂੰ ਚੀਨੀ ਹਿਸਾਬਕਾਰ, ਹੂ ਸਾਂਗ ਸੁਆਂਗ ਸੂ ਨੇ ਵਰਤਿਆ ਸੀ । ਫ਼ਿਰ ਇਹਨਾਂ ਨੂੰ ਹੀਜ਼ਨਬਰਗ,ਪਾਸਕਲ ਆਦਿ ਵਰਗੇ ਵਿਗਿਆਨੀਆਂ ਨੇ ਵੀ ਅਪਣੀ ਕੰਮ ਵਿਚ ਵਰਤਿਆ ਸੀ ।

ਜਮ੍ਹਾ

$\begin{bmatrix} 1 & 3 & 1 \\ 1 & 0 & 0 \end{bmatrix} + \begin{bmatrix} 0 & 0 & 5 \\ 7 & 5 & 0 \end{bmatrix} = \begin{bmatrix} 1+0 & 3+0 & 1+5 \\ 1+7 & 0+5 & 0+0 \end{bmatrix} = \begin{bmatrix} 1 & 3 & 6 \\ 8 & 5 & 0 \end{bmatrix}$

ਗੁਣਾ

$2 \cdot \begin{bmatrix} 1 & 8 & -3 \\ 4 & -2 & 5 \end{bmatrix} = \begin{bmatrix} 2 \cdot 1 & 2\cdot 8 & 2\cdot -3 \\ 2\cdot 4 & 2\cdot -2 & 2\cdot 5 \end{bmatrix} = \begin{bmatrix} 2 & 16 & -6 \\ 8 & -4 & 10 \end{bmatrix}$

ਹਵਾਲੇ

• Arnold, V. I.; Cooke, Roger (1992), Ordinary differential equations, Berlin, New York: Springer-Verlag, ISBN 978-3-540-54813-3 
• Artin, Michael (1991), Algebra, Prentice Hall, ISBN 978-0-89871-510-1 
• Association for Computing Machinery (1979), Computer Graphics, Tata McGraw-Hill, ISBN 978-0-07-059376-3 
• Baker, Andrew J. (2003), Matrix Groups: An Introduction to Lie Group Theory, Berlin, New York: Springer-Verlag, ISBN 978-1-85233-470-3 
• Bau III, David; Trefethen, Lloyd N. (1997), Numerical linear algebra, Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-361-9 
• Bretscher, Otto (2005), Linear Algebra with Applications (3rd ed.), Prentice Hall 
• Bronson, Richard (1989), Schaum's outline of theory and problems of matrix operations, New York: McGraw-Hill, ISBN 978-0-07-007978-6 
• Brown, William A. (1991), Matrices and vector spaces, New York: M. Dekker, ISBN 978-0-8247-8419-5 
• Coburn, Nathaniel (1955), Vector and tensor analysis, New York: Macmillan, OCLC 1029828 
• Conrey, J. B. (2007), Ranks of elliptic curves and random matrix theory, Cambridge University Press, ISBN 978-0-521-69964-8 
• Fudenberg, D.; Tirole, Jean (1983), Game Theory, MIT Press 
• Gilbarg, David; Trudinger, Neil S. (2001), Elliptic partial differential equations of second order (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-3-540-41160-4 
• Godsil, Chris; Royle, Gordon (2004), Algebraic Graph Theory, Graduate Texts in Mathematics, 207, Berlin, New York: Springer-Verlag, ISBN 978-0-387-95220-8 
• Golub, Gene H.; Van Loan, Charles F. (1996), Matrix Computations (3rd ed.), Johns Hopkins, ISBN 978-0-8018-5414-9 
• Greub, Werner Hildbert (1975), Linear algebra, Graduate Texts in Mathematics, Berlin, New York: Springer-Verlag, ISBN 978-0-387-90110-7 
• Halmos, Paul Richard (1982), A Hilbert space problem book, Graduate Texts in Mathematics, 19 (2nd ed.), Berlin, New York: Springer-Verlag, MR675952ਫਰਮਾ:Only in print, ISBN 978-0-387-90685-0 
• Horn, Roger A.; Johnson, Charles R. (1985), Matrix Analysis, Cambridge University Press, ISBN 978-0-521-38632-6 
• Householder, Alston S. (1975), The theory of matrices in numerical analysis, New York: Dover Publications, MR0378371ਫਰਮਾ:Only in print 
• Krzanowski, W. J. (1988), Principles of multivariate analysis, Oxford Statistical Science Series, 3, The Clarendon Press Oxford University Press, MR969370ਫਰਮਾ:Only in print, ISBN 978-0-19-852211-9 
• Itõ, Kiyosi, ed. (1987), Encyclopedic dictionary of mathematics. Vol. I--IV (2nd ed.), MIT Press, MR901762ਫਰਮਾ:Only in print, ISBN 978-0-262-09026-1 
• Lang, Serge (1969), Analysis II, Addison-Wesley 
• Lang, Serge (1987a), Calculus of several variables (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-96405-8 
• Lang, Serge (1987b), Linear algebra, Berlin, New York: Springer-Verlag, ISBN 978-0-387-96412-6 
• Lang, Serge (2002), Algebra, Graduate Texts in Mathematics, 211 (Revised third ed.), New York: Springer-Verlag, MR1878556ਫਰਮਾ:Only in print, ISBN 978-0-387-95385-4 
• Latouche, G.; Ramaswami, V. (1999), Introduction to matrix analytic methods in stochastic modeling (1st ed.), Philadelphia: Society for Industrial and Applied Mathematics, ISBN 978-0-89871-425-8 
• Manning, Christopher D.; Schütze, Hinrich (1999), Foundations of statistical natural language processing, MIT Press, ISBN 978-0-262-13360-9 
• Mehata, K. M.; Srinivasan, S. K. (1978), Stochastic processes, New York: McGraw-Hill, ISBN 978-0-07-096612-3 
• Mirsky, Leonid (1990), An Introduction to Linear Algebra, Courier Dover Publications, ISBN 978-0-486-66434-7, http://books.google.de/books?id=ULMmheb26ZcC&pg=PA1&dq=linear+algebra+determinant&lr=lang_en&as_brr=3&as_pt=ALLTYPES#PPA16,M1 
• Nocedal, Jorge; Wright, Stephen J. (2006), Numerical Optimization (2nd ed.), Berlin, New York: Springer-Verlag, p. 449, ISBN 978-0-387-30303-1 
• Oualline, Steve (2003), Practical C++ programming, O'Reilly, ISBN 978-0-596-00419-4 
• Press, William H.; Flannery, Brian P.; Teukolsky, Saul A.; Vetterling, William T. (1992), "LU Decomposition and Its Applications", Numerical Recipes in FORTRAN: The Art of Scientific Computing (2nd ed.), Cambridge University Press, pp. 34–42, http://www.mpi-hd.mpg.de/astrophysik/HEA/internal/Numerical_Recipes/f2-3.pdf 
• Punnen, Abraham P.; Gutin, Gregory (2002), The traveling salesman problem and its variations, Boston: Kluwer Academic Publishers, ISBN 978-1-4020-0664-7 
• Reichl, Linda E. (2004), The transition to chaos: conservative classical systems and quantum manifestations, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98788-0 
• Rowen, Louis Halle (2008), Graduate Algebra: noncommutative view, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-4153-2 
• Šolin, Pavel (2005), Partial Differential Equations and the Finite Element Method, Wiley-Interscience, ISBN 978-0-471-76409-0 
• Stinson, Douglas R. (2005), Cryptography, Discrete Mathematics and Its Applications, Chapman & Hall/CRC, ISBN 978-1-58488-508-5 
• Stoer, Josef; Bulirsch, Roland (2002), Introduction to Numerical Analysis (3rd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-95452-3 
• Ward, J. P. (1997), Quaternions and Cayley numbers, Mathematics and its Applications, 403, Dordrecht: Kluwer Academic Publishers Group, MR1458894ਫਰਮਾ:Only in print, ISBN 978-0-7923-4513-8 
• Wolfram, Stephen (2003), The Mathematica Book (5th ed.), Champaign, Ill: Wolfram Media, ISBN 978-1-57955-022-6 

ਬਾਹਰੀ ਲਿੰਕ

ਪਿਛੋਕੜ

• MacTutor: Matrices and determinants
• Matrices and Linear Algebra on the Earliest Uses Pages
• Earliest Uses of Symbols for Matrices and Vectors

ਕਿਤਾਬਾਂ

• Kaw, Autar K., Introduction to Matrix Algebra, ISBN 978-0-615-25126-4, http://autarkaw.com/books/matrixalgebra/index.html 
• The Matrix Cookbook, http://matrixcookbook.com, retrieved on ੧੦ ਦਸੰਬਰ ੨੦੦੮ 
• Brookes, M. (2005), The Matrix Reference Manual, London: Imperial College, http://www.ee.ic.ac.uk/hp/staff/dmb/matrix/intro.html, retrieved on ੧੦ ਦਸੰਬਰ ੨੦੦੮ 

ਮੈਟ੍ਰਿਕਸ ਕੈਲਕੁਲੇਟਰ

• SuperiorMath (Matrix Calculator), http://www.webalice.it/simoalessia/SuperiorMath/matrix.html 
• Matrix Calculator (DotNumerics ), http://www.dotnumerics.com/MatrixCalculator/ 
• Xiao, Gang, Matrix calculator, http://wims.unice.fr/wims/wims.cgi?module=tool/linear/matrix.en, retrieved on ੧੦ ਦਸੰਬਰ ੨੦੦੮ 
• Online matrix calculator, http://www.bluebit.gr/matrix-calculator/, retrieved on ੧੦ ਦਸੰਬਰ ੨੦੦੮ 
• Online matrix calculator(ZK framework), http://matrixcalc.info/MatrixZK/, retrieved on ੨੬ ਨਵੰਬਰ ੨੦੦੯ 

• Oehlert, Gary W.; Bingham, Christopher, MacAnova, University of Minnesota, School of Statistics, http://www.stat.umn.edu/macanova/macanova.home.html, retrieved on ੧੦ ਦਸੰਬਰ ੨੦੦੮ , a freeware package for matrix algebra and statistics
• Online matrix calculator, http://www.idomaths.com/matrix.php, retrieved on ੧੪ ਦਸੰਬਰ ੨੦੦੯ 
• Online calculator - Operation with matrices in R (determinant, track, inverse, adjoint, transpose)