Algebra Cast operations

 30 August 16:29   

    Two matrices can be added calm alone if they accept the aforementioned ambit (the aforementioned amount of rows and columns). The resultant cast is artlessly the cast whose elements are the sum of the elements in the two matrices that were added together. If a cast $A$ is added to a cast $B$ and the resultant cast is $C$, then $c\_\; =\; a\_\; +\; b\_$.

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     5 & 1 & 7 3 & 9 & 4 0 & -2 & 6

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     +

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     3 & 2 & 4 7 & 1 & -3 4 & 5 & 6

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     =

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     8 & 3 & 11 10 & 10 & 1 4 & 3 & 12

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    Two matrices may be assorted calm alone if the amount of columns in the first cast is according to the rows in the additional matrix. That is, if the first cast is $n\; imes\; m$, then the additional cast haveto be $m\; imes\; p$. The consistent cast will accept a ambit of $n\; imes\; p$, area anniversary aspect is the sum of the articles of the entries in a row of the first cast with the entries of the agnate cavalcade in the additional matrix. If $C=AB$, then $c\_\; =\; sum\_^na\_b\_$.

    Although cast multiplication is not commutative, it is associative, which agency that (AB)C=A(BC). Back cast multiplication is not commutative, the adjustment of the factors haveto be specified. AB would be apprehend as A post-multiplied by B or B premultiplied by A. Cast multiplication obeys the distributive property, so A(B+C)=AB+AC. Also, two nonzero matrices do not necessarily accept a nonzero product.

    There is no such affair as Cast Division. To bisect out a matrix, you charge first to access the changed of the matrix, and then accumulate by the inverse. We altercate inverses below.

    To access the alter of a matrix, we bandy the rows and the colums of that matrix. If we accept a cast X, the alter is denoted X^T. For example:

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    The account of a matrix, X is denoted by |X|.

    If the cast has a non-zero determinant, the cast is said to be invertable. Changed matrices chase the accustomed formula:

    :$XX^\; =\; X^X\; =\; I$

    Where I is the character matrix.