I had previously often assumed that it means a matrix to matrix operation, but I now think that it almost never does, but instead it usually means matrix to vector multiplication.

Then the term tensor is used too. As an EE I know vector fields where a 4D input vector place and time is transformed into a 3D vector of complex numbers phasor, Poynting vector output. I suppose that is a tensor. But I do not understand what a tensor is in AI.

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So, in what context do they mean what and does the HW actually have to deal with two matrices or one or is it actually just loads of dot products? The first two angles - problems and algorithms - are tightly coupled. Typical matrix problems we want to solve as an end-goal:. Both types of dot products are algorithmically trivial.

Most of the heavy lifting in matrix solve algorithms is done by breaking A into blocks, and then doing square matrix multiplications on those blocks. Strassen's algorithm is often used at the block level to improve big-O runtime for large matrix multiplies. I'm not a hardware expert, but my understanding is that hardware is usually optimized to make multiplication of square matrices of a certain size very fast.

Vector notation

This is largely about caching - you want caches to be large enough to hold the matrices in question. Fancy libraries know how large the cache is, and choose block sizes accordingly. Other fancy libraries use algorithms which perform close-to-optimally for any cache size, by accessing things in a pattern which plays well with any cache.

The other factor, of course, is just having lots of hardware multipliers. In practice, these often have block structure, so we still need to fall back on normal matrix-multiplication-based algorithms for the blocks themselves.

As for "matrix" vs "tensor" It does not imply the sort of transformation properties we associate with "tensors" in e. A vector can be viewed as a particular sort of a matrix, with one dimension equal to 1. So matrix-vector multiplications are a special case of matrix-matrix multiplications. A tensor is a possibly-higher-dimensional generalization of a matrix.Sign in to comment. Sign in to answer this question. Unable to complete the action because of changes made to the page.

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Multiplying a Vector by a Matrix

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Omar A Jimenez on 19 Nov Vote 0. Commented: Walter Roberson on 29 Aug Accepted Answer: Walter Roberson. I have these two vectors. Thanks in advance. Stephen Cobeldick on 19 Nov Cancel Copy to Clipboard.

It only takes a minute to sign up. Following the probable definition from How do I typeset vertical and horizontal lines inside a matrix? Sign up to join this community. The best answers are voted up and rise to the top.

Home Questions Tags Users Unanswered. Multiplication of vector and matrix Ask Question. Asked 2 years ago. Active 2 years ago.

Viewed 10k times. Daniel Yefimov. Daniel Yefimov Daniel Yefimov 1 1 gold badge 1 1 silver badge 5 5 bronze badges.

Zarko who does you copy me? Sebastiano, i'm lost in code Honestly, I did not understand anything about what the user wants to do. Active Oldest Votes. AboAmmar AboAmmar Is there also a magical definition? I upvote the magical command. You can use this code substituting in place of the letters what you want.

Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. The Overflow Blog. Featured on Meta. Community and Moderator guidelines for escalating issues via new response…. Feedback on Q2 Community Roadmap. Linked Related 7. Hot Network Questions. Question feed.In excel we have an inbuilt function for matrix multiplication and it is MMULT function, it takes two arrays as an argument and returns the product of two arrays, given that both the arrays should have the same number of rows and the same number of columns.

Matrix multiplication is one of the useful features of excel presented to do mathematical operations. It helps to gain the product of two matrices. The matrices that want to multiply have a certain number of rows and columns to present the data. The size of the resulted matrix is taken from the number of rows of the first array and the number of columns of the second array.

There is a condition to matrix multiplication; the number of columns in the first matrix should be equal to the number of rows in the second matrix. To perform the matrix multiplication, the predefined MMULT function presented in the excel software is used.

Excel matrix multiplication reduces a lot of time incurred in calculating the product of matrices manually. In general, matrix multiplication is done in two ways. Simple scalar multiplication is performed by using the basic arithmetic operations and advanced matrices multiplication is managed with the help of array functions.

It is one of the predefined excel function used in worksheets to perform calculations in a short time.

Multiplying a vector by a scalar - Vectors and spaces - Linear Algebra - Khan Academy

Matrices multiplication in excel has some real-time application. There are two ways to do matrix multiplication. Below are some examples of the Excel Matrix Multiplication. The results obtained by multiplying two arrays as follows and the size of the resultant array is 3X3. Matrix Multiplication between arrays with a single row and single column.

Let consider the elements of matrices as.

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So Enter the Matrix Multiplication formula in the cell. This has been a guide to Excel Matrix Multiplication. You can learn more about excel from the following articles —.

Change your preferences any time. Stack Overflow for Teams is a private, secure spot for you and your coworkers to find and share information. Here we define x1 as a vector, I assume R default vector is a column vector? Then we define x2 is a transpose of x1which the display also seems strange for me.

Now, my question is that, x1 and x2 are completely different things one is transpose of anotherbut we have the same results here. A numeric vector of length 3 is NOT a "column vector" in the sense that it does not have a dimension. Treating an atomic vector on the same footing as a matrix of dimension n x 1 matrix makes sense because R handles its matrix operations with column-major indexing.

And R associativity rules proceed from left to right, so this also succeeds:. I think you should read the? Contrary to t, transpose processes vectors as if they were row matrices.

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Matrix and vector multiplication operation in R Ask Question. Asked 3 years, 8 months ago. Active 3 years, 8 months ago. Viewed 6k times. I feel matrix operations in R is very confusing: we are mixing row and column vectors. Finally, if we define x3 as a matrix the display seems better. Any explanations? Cyrus Mohammadian 3, 4 4 gold badges 22 22 silver badges 46 46 bronze badges.

Active Oldest Votes. If one argument is a vector, it will be promoted to either a row or column matrix to make the two arguments conformable. If both are vectors of the same length, it will return the inner product as a matrix. Gregor Thomas Weihuang Wong Weihuang Wong To multiply a row vector by a column vector, the row vector must have as many columns as the column vector has rows.

Let us define the multiplication between a matrix A and a vector x in which the number of columns in A equals the number of rows in x. In other words, the number of rows in A determines the number of rows in the product b. By the definition, number of columns in A equals the number of rows in y. First, multiply Row 1 of the matrix by Column 1 of the vector.

Next, multiply Row 2 of the matrix by Column 1 of the vector. Finally multiply Row 3 of the matrix by Column 1 of the vector.

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Varsity Tutors connects learners with experts. Instructors are independent contractors who tailor their services to each client, using their own style, methods and materials. Multiplying a Vector by a Matrix To multiply a row vector by a column vector, the row vector must have as many columns as the column vector has rows.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. I have always dealt with vector - matrix multiplication where the vector is the right multiplicand, but I am not sure how to apply the product between a matrix and a vector when the vector is the left multiplicand.

Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How to multiply a vector from the left side with matrix?

Ask Question. Asked 4 years, 3 months ago. Active 2 years ago. Viewed 15k times.

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If the vector is on the left, the result is a projection of the vector onto the columns of the matrix. Active Oldest Votes. Alekos Robotis Alekos Robotis Each resulting scalar is the corresponding entry in the resulting row vector.