mtimes,*

Matrix multiplication

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Syntax

C = A*B

C = mtimes(A,B)

Description

example

C=A*B矩阵乘积的吗AandB. IfAis an m-by-p andBis a p-by-n matrix, thenCis an m-by-n matrix defined by

$C (i, j) = \sum_{k = 1}^{p} A (i, k) B (k, j) .$

This definition says thatC(i,j)is the inner product of theith row ofAwith thejth column ofB. You can write this definition using the MATLAB^®colon operator as

C(i,j) = A(i,:)*B(:,j)

For nonscalarAandB, the number of columns ofAmust equal the number of rows ofB. Matrix multiplication isnotuniversally commutative for nonscalar inputs. That is,A*Bis typically not equal toB*A. If at least one input is scalar, thenA*B是equivalent toA.*Band is commutative.

C= mtimes(A,B)is an alternative way to executeA*B, but is rarely used. It enables operator overloading for classes.

Examples

collapse all

Multiply Two Vectors

Open Live Script

Create a 1-by-4 row vector,A, and a 4-by-1 column vector,B.

A = [1 1 0 0]; B = [1; 2; 3; 4];

MultiplyAtimesB.

C = A*B

C = 3

The result is a 1-by-1 scalar, also called the点productorinner productof the vectorsAandB. Alternatively, you can calculate the dot product $A \cdot B$ with the syntax点(A,B).

MultiplyBtimesA.

C = B*A

C =4×41 1 0 0 2 2 0 0 3 3 0 0 4 4 0 0

The result is a 4-by-4 matrix, also called theouter productof the vectorsAandB. The outer product of two vectors, $A \otimes B$ , returns a matrix.

Multiply Two Arrays

Open Live Script

Create two arrays,AandB.

A = [1 3 5; 2 4 7]; B = [-5 8 11; 3 9 21; 4 0 8];

Calculate the product ofAandB.

C = A*B

C =2×324 35 114 30 52 162

Calculate the inner product of the second row ofAand the third column ofB.

A(2,:)*B(:,3)

ans = 162

This answer is the same asC(2,3).

Input Arguments

collapse all

`A`,`B`—Operands
scalars|vectors|matrices

Operands, specified as scalars, vectors, or matrices.

If at least one input is scalar, thenA*B是equivalent toA.*B. In this case, the nonscalar array can be any size.
For nonscalar inputs,AandBmust be 2-D arrays where the number of columns inAmust be equal to the number of rows inB.
If one ofAorBis an integer class (int16,uint8, …), then the other input must be a scalar. Operands with an integer data type cannot be complex.

Output Arguments

collapse all

`C`— Product
scalar | vector | matrix

Product, returned as a scalar, vector, or matrix. ArrayChas the same number of rows as inputAand the same number of columns as inputB. For example, ifAis an m-by-0 empty matrix andBis a 0-by-n empty matrix, thenA*Bis an m-by-n matrix of zeros.

Tips

With chained matrix multiplications such asA*B*C, you might be able to improve execution time by using parentheses to dictate the order of the operations. Consider the case of multiplying three matrices withA*B*C, whereAis 500-by-2,Bis 2-by-500, andCis 500-by-2.
- With no parentheses, theorder of operationsis left to right soA*Bis calculated first, which forms a 500-by-500 matrix. This matrix is then multiplied withCto arrive at the 500-by-2 result.
- If you instead specifyA*(B*C), thenB*Cis multiplied first, producing a 2-by-2 matrix. The small matrix then multipliesAto arrive at the same 500-by-2 result, but with fewer operations and less intermediate memory usage.

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

This function supports tall arrays with the limitations:

ForA*BwhereAandBare both tall arrays, one of them must be a scalar.
ForA'*B, bothAandBmust be tall vectors or matrices with a common size in the first dimension.

For more information, seeTall Arrays.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Multiplication of pure imaginary numbers by non-finite numbers might not match MATLAB. The code generator does not specialize multiplication by pure imaginary numbers—it does not eliminate calculations with the zero real part. For example,(正+ 1i)*1i = (Inf*0 – 1*1) + (Inf*1 + 1*0)i = NaN + Infi.
SeeVariable-Sizing Restrictions for Code Generation of Toolbox Functions(MATLAB Coder).

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

Multiplication of pure imaginary numbers by non-finite numbers might not match MATLAB. The code generator does not specialize multiplication by pure imaginary numbers—it does not eliminate calculations with the zero real part. For example,(正+ 1i)*1i = (Inf*0 – 1*1) + (Inf*1 + 1*0)i = NaN + Infi.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

This function fully supports thread-based environments. For more information, seeRun MATLAB Functions in Thread-Based Environment.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

64-bit integers are not supported.

For more information, seeRun MATLAB Functions on a GPU(Parallel Computing Toolbox).

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, seeRun MATLAB Functions with Distributed Arrays(Parallel Computing Toolbox).

mtimes,*

Syntax

Description

Examples

Multiply Two Vectors

Multiply Two Arrays

Input Arguments

`A`,`B`—Operands
scalars|vectors|matrices

Output Arguments

`C`— Product
scalar | vector | matrix

Tips

Extended Capabilities

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

Topics

MATLAB Documentation

金宝app

Introducing Deep Learning with MATLAB

mtimes,*

Syntax

Description

Examples

Multiply Two Vectors

Multiply Two Arrays

Input Arguments

A,B—Operandsscalars|vectors|matrices

Output Arguments

C— Productscalar | vector | matrix

Tips

Extended Capabilities

Tall ArraysCalculate with arrays that have more rows than fit in memory.

C/C++ Code GenerationGenerate C and C++ code using MATLAB® Coder™.

GPU Code GenerationGenerate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code GenerationGenerate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Thread-Based EnvironmentRun code in the background using MATLAB®backgroundPoolor accelerate code with Parallel Computing Toolbox™ThreadPool.

GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed ArraysPartition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

See Also

Topics

MATLAB Documentation

金宝app

Introducing Deep Learning with MATLAB

`A`,`B`—Operands
scalars|vectors|matrices

`C`— Product
scalar | vector | matrix

Tall Arrays
Calculate with arrays that have more rows than fit in memory.

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

Thread-Based Environment
Run code in the background using MATLAB®`backgroundPool`or accelerate code with Parallel Computing Toolbox™`ThreadPool`.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.