Dot product là gì

Other than the matrix multiplication discussed earlier, vectors could be multiplied by two more methods : Dot sản phẩm và Hadamard Product. Results obtained from both methods are different.Quý khách hàng đang xem: Dot hàng hóa là gì

Dot Product

The elements corresponding to lớn same row and column are multiplied together & the products are added such that, the result is a scalar.

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Dot product of vectors a, b and c

Unlike matrix multiplication the result of dot hàng hóa is not another vector or matrix, it is a scalar.



Dot product of vector ab

Order of vectors does not matter for dot product, just the number of elements in both vectors should be equal.

The geometric formula of dot product is


Here |a| và |b| are magnitude of vector ab and they are multiplied with cosine of angle between vectors

Dot product is also called inner hàng hóa or scalar sản phẩm.

Projection of Vector

Assuming that we have sầu two vectors c and d, subtended by angle, phi(Ф).

Vector c with subscript-ed d represents projection of vector c on vector d

We can conclude from figure that the projection is equal khổng lồ the horizontal component of vector c with respect to the angle phi(Ф).

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Projections have sầu wide use in linear algebra & machine learning (Support Vector Machine(SVM) is a machine learning algorithm, used for classification of data).

Hadamard Product (Element -wise Multiplication)

Hadamard sản phẩm of two vectors is very similar to matrix addition, elements corresponding khổng lồ same row and columns of given vectors/matrices are multiplied together to form a new vector/matrix.

It is named after French Mathematician, Jacques Hadamard.

Hadamard hàng hóa of vector g, hm

The order of matrices/vectors khổng lồ be multiplied should be same and the resulting matrix will also be of same order.

Matrix N is of same order as input đầu vào matrices (2x3)

Hadamard product is used in image compression techniques such as JPEG. It is also known as Schur hàng hóa after German Mathematician, Issai Schur.

Additional Resources :

Dot Product

Vector Projection

Hadamard Product

Jacques Hadamard

Iskhông đúng Schur

Use of Hadamard sản phẩm in JPEG


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I write about Maths, CS, ML, Statistics & Productivity | | the concepts of Linear Algebra và their application. View the complete series (in order) here :ên mục: Hỏi Đáp