Linked Questions

11
votes
4answers
2k views

Why multiplication of matrix is not done in the same way as matrix addition (i.e. adding corresponding entries)? [duplicate]

Why multiplication of matrix is not done in the same way as matrix addition (i.e. adding corresponding entries)? I know it is related to linear transformation, but by reading book I'm unable to ...
11
votes
3answers
793 views

Why is the matrix multiplication defined as it is? [duplicate]

Matrix multiplication is defined as: Let $A$ be a $n \times m$ matrix and $B$ a $m\times p$ matrix, the product $AB$ is defined as a matrix of size $n\times p$ such that $(AB)_i,_j = \sum\limits_{k=...
3
votes
2answers
1k views

Why is matrix multiplication defined a certain way? [duplicate]

Why is it that when multiplying a (1x3) by (3x1) matrix, you get a (1x1) matrix, but when multiplying a (3x1) matrix by a (1x3) matrix, you get a (3x3) matrix? Why is matrix multiplication defined ...
1
vote
5answers
53 views

Why can't we multiply matrices entrywise? [duplicate]

Why can't we multiply corresponding elements like addition is done? Is there a specific reason why it won't be significant? By definition, we have to multiply a row by columns. Why such a ...
2
votes
0answers
48 views

Multiplication of matrices [duplicate]

When we add two matrices we just simply add the corresponding elements but when we multiply two matrices there is a much more complex process.Why does it happens?
87
votes
3answers
19k views

Why, historically, do we multiply matrices as we do?

Multiplication of matrices — taking the dot product of the $i$th row of the first matrix and the $j$th column of the second to yield the $ij$th entry of the product — is not a very ...
45
votes
2answers
24k views

Matrix multiplication: interpreting and understanding the process

I have just watched the first half of the 3rd lecture of Gilbert Strang on the open course ware with link: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/ It ...
5
votes
4answers
338 views

Intuition behind multiplication

I recently read this post and the highest voted comment and it got me thinking. How does think about multiplication if it is decimals? For example, if we have $3.9876542 \times 2.3156479$ then how ...
2
votes
2answers
5k views

Definition of matrix-vector multiplication

I have just learned about matrix-vector multiplication.Is there a particular reason why we multiply a matrix by a column vector instead of a row vector? For example $Ax = \begin{bmatrix}a&b\\c&...
5
votes
2answers
873 views

Why is Matrix Multiplication Not Defined Like This? [duplicate]

I'm sure everyone already thought about this at least one time. Why matrix multiplication is not defined the way showed below? $$\left( \begin{array}{ccc} a_{11} & a_{12} & \ldots \\ a_{21} &...
5
votes
1answer
1k views

What does matrix multiplication have to do with scalar multiplication?

Why are matrix and scalar multiplication denoted the same way and treated as the same operation in standard mathematical notation? This is always a source of confusion for me because they have ...
3
votes
2answers
446 views

Matrix Multiplication - Why Rows $\cdot$ Columns = Columns?

I'm nearing the end of my first year of Calculus and am pretty confident in the parts of it I've learned, yet I still don't have a good understanding of matrices, which seem like they should be easier ...
1
vote
2answers
526 views

Is “basis times square matrix” a new basis?

Suppose we have a vector space $V = (K, +, \cdot)$. Let $B$ be a basis for $V$. Now we take an arbitrary square matrix $S \neq 0$. $BS$ is just a linear combination of $B$. Thus $BS$ should be a new ...
6
votes
1answer
247 views

Morphism between matrices and linear equations

I'm currently a beginner at linear algebra. So, in some books I see authors start defining linear equations and then they define matrices and, supposedly, the definition of associative matrix is to ...
2
votes
1answer
216 views

show that $((GL(2,\mathbb{R}),\bullet)$ is a group

Let $G(2,\mathbb R)=\{\text{All invertible }2 \times 2\text{ matrices over }\mathbb{R}\}$. Then i want to show that $((G(2,\mathbb{R}),\bullet)$ is a group, where $\bullet$ is multiplication of ...

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