Matrix Algebra

Matrix Algebra - Note on Matrix Algebra Definition 1: a11...

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Matrix - 1 Note on Matrix Algebra Definition 1: 11 12 1 21 22 2 12 ... ... :: : ... n n mm m n aa a a A a ⎛⎞ ⎜⎟ = ⎝⎠ . A is called a m × n matrix. (m = # of rows ; n = # of column.) Definition 2: Let A be an m × n matrix. The transpose of A is denoted by A t (or A ), which is a n × m matrix; and it is obtained by the following procedure. 1st column of A 1st row of A t 2nd column of A 2st column of A t ... etc. [EXAMPLE] 23 32 26 214 ;1 3 633 43 t AA × × == . Definition 3: Let A be a m × n matrix. If m = n, A is called a square matrix. [EXAMPLE] 24 35 A = .
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Matrix - 2 Definition 4: Let A be an m × n matrix. If all the a ij = 0, then A is called a zero matrix. [EXAMPLE] 00 ; 01 AB ⎛⎞⎛⎞ ⎜⎟⎜⎟ == ⎝⎠⎝⎠ . A is not a zero matrix but B is. Definition 5: Let A be a square matrix. A is call an identity matrix if all the diagonal entries are one and all the off-diagonals are zero. [EXAMPLE] 3 100 010 001 I ⎛⎞ ⎜⎟ = ⎝⎠ . Definition 6: Let A be a square matrix. A is called symmetric if and only if A = A t (or A ).
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Matrix - 3 [EXAMPLE] 134 321 411 t AA ⎛⎞ ⎜⎟
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Matrix Algebra - Note on Matrix Algebra Definition 1: a11...

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