Matrices

Could anyone please explain why matrix multiplication is defined in such a weird way?

#HelpMe! #Advice #Math

Note by Pranav Chakravarthy
8 years, 4 months ago

No vote yet
4 votes

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Comments

Found this.

Zi Song Yeoh - 8 years, 4 months ago

Instead of being weird, it's actually very natural. Matrices are meant to represent linear maps, and using that information would help you understand why matrix multiplication (and addition) is defined as such.

For example, if I have 2 linear maps f:R3R2,g:R2R3f: \mathbb{R}^3 \rightarrow \mathbb{R}^2, g: \mathbb{R}^2 \rightarrow \mathbb{R}^3 given by f(a,b,c)=(11a+12b+13c,21a+22b+23c) f( a, b, c) = (11a + 12b +13c, 21a + 22b + 23c) and g(x,y)=(99x+98y,89x+88y,79x+78y) g( x, y) = (99x + 98 y, 89x + 88 y, 79x + 78 y) , what is the value of g(f(a,b,c)) g (f (a, b, c)) and f(g(x,y)) f(g(x, y) ) ? If you do not expand the terms [Treat 1111 as a11 a_{11} ], you will find that the composition of these linear maps results in matrix multiplication.

Repeat the above for the appropriate scenario to relate the addition of 2 linear maps (f+g)(x)=f(x)+g(x) (f+g) (x) = f(x) + g(x) to matrix addition.

Calvin Lin Staff - 8 years, 4 months ago

it is just a row space by column space multiplication and summation of all such possible multiplications .......

Jaydutt Kulkarni - 8 years, 4 months ago
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