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A Matrix

A matrix is a rectangular array of numbers or symbols used to represent systems of equations or transformations, characterized by rows and columns. Key types include zero, identity, diagonal, symmetric, and skew-symmetric matrices, with operations such as addition, scalar multiplication, and matrix multiplication. Matrices have applications in linear algebra, computer graphics, machine learning, physics, engineering, and data analysis.

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MALISON SALIMA
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9 views2 pages

A Matrix

A matrix is a rectangular array of numbers or symbols used to represent systems of equations or transformations, characterized by rows and columns. Key types include zero, identity, diagonal, symmetric, and skew-symmetric matrices, with operations such as addition, scalar multiplication, and matrix multiplication. Matrices have applications in linear algebra, computer graphics, machine learning, physics, engineering, and data analysis.

Uploaded by

MALISON SALIMA
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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A matrix is a mathematical representation of a system of equations or a transformation, consisting of a

rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

Key Concepts:

1. *Rows and columns*: A matrix has rows (horizontal) and columns (vertical).

2. *Entries*: The individual elements within a matrix are called entries.

3. *Dimension*: The size of a matrix is described by its dimension, e.g., 2x3 or 3x4.

4. *Square matrix*: A matrix with the same number of rows and columns.

Types of Matrices:

1. *Zero matrix*: A matrix filled with zeros.

2. *Identity matrix*: A square matrix with ones on the main diagonal and zeros elsewhere.

3. *Diagonal matrix*: A square matrix with non-zero entries only on the main diagonal.

4. *Symmetric matrix*: A square matrix that is equal to its transpose.

5. *Skew-symmetric matrix*: A square matrix whose transpose is its negative.

Matrix Operations:

1. *Addition*: Adding corresponding entries of two matrices.

2. *Scalar multiplication*: Multiplying each entry of a matrix by a scalar.

3. *Matrix multiplication*: Multiplying two matrices to form a new matrix.

4. *Transpose*: Swapping the rows and columns of a matrix.

Applications of Matrices:

1. *Linear algebra*: Matrices are used to represent systems of linear equations and to solve them.

2. *Computer graphics*: Matrices are used to perform transformations on images and 3D models.
3. *Machine learning*: Matrices are used to represent data and to perform operations such as matrix
multiplication.

4. *Physics and engineering*: Matrices are used to describe the behavior of physical systems, such as
electrical circuits and mechanical systems.

5. *Data analysis*: Matrices are used in statistics and data analysis to represent and manipulate data.

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