Transpose and Conjugate Transpose Properties of Transposition 命电有这女子 Matrix Theory Matrix Transposition and Related -7/30
Transpose and Conjugate Transpose Properties of Transposition ▸ For real matrices, the conjugate transpose and the transpose are identical. ▸ Transposing a matrix twice gives back the original, (A T ) T = A, (A H ) H = A. ▸ Transposition does not affect a scalar, ▸ The transpose of a sum is the sum of the transposes, (A + B) T = A T + B T , (A + B) H = A H + B H . ▸ The transpose of a product is the product of the transposes with the factors in reverse order, (AB) T = B T A T , (AB) H = B HA H . Matrix Theory Matrix Transposition and Related - 7/30
Transpose and Conjugate Transpose Properties of Transposition For real matrices,the conjugate transpose and the transpose are identical. 命电有这女子 Matrix Theory Matrix Transposition and Related -7/30
Transpose and Conjugate Transpose Properties of Transposition ▸ For real matrices, the conjugate transpose and the transpose are identical. ▸ Transposing a matrix twice gives back the original, (A T ) T = A, (A H ) H = A. ▸ Transposition does not affect a scalar, ▸ The transpose of a sum is the sum of the transposes, (A + B) T = A T + B T , (A + B) H = A H + B H . ▸ The transpose of a product is the product of the transposes with the factors in reverse order, (AB) T = B T A T , (AB) H = B HA H . Matrix Theory Matrix Transposition and Related - 7/30
Transpose and Conjugate Transpose Properties of Transposition For real matrices,the conjugate transpose and the transpose are identical.That is,if AeRmx,then AH=AT. 命电有这女子 Matrix Theory Matrix Transposition and Related -7/30
Transpose and Conjugate Transpose Properties of Transposition ▸ For real matrices, the conjugate transpose and the transpose are identical. That is, if A ∈ R m×n , then A H = A T . ▸ Transposing a matrix twice gives back the original, (A T ) T = A, (A H ) H = A. ▸ Transposition does not affect a scalar, ▸ The transpose of a sum is the sum of the transposes, (A + B) T = A T + B T , (A + B) H = A H + B H . ▸ The transpose of a product is the product of the transposes with the factors in reverse order, (AB) T = B T A T , (AB) H = B HA H . Matrix Theory Matrix Transposition and Related - 7/30
Transpose and Conjugate Transpose Properties of Transposition For real matrices,the conjugate transpose and the transpose are identical.That is,if AeRmx,then AH=AT. Transposing a matrix twice gives back the original, (AT)T=A, (AH)H=A. 命电有这女子 Matrix Theory Matrix Transposition and Related -7/30
Transpose and Conjugate Transpose Properties of Transposition ▸ For real matrices, the conjugate transpose and the transpose are identical. That is, if A ∈ R m×n , then A H = A T . ▸ Transposing a matrix twice gives back the original, (A T ) T = A, (A H ) H = A. ▸ Transposition does not affect a scalar, ▸ The transpose of a sum is the sum of the transposes, (A + B) T = A T + B T , (A + B) H = A H + B H . ▸ The transpose of a product is the product of the transposes with the factors in reverse order, (AB) T = B T A T , (AB) H = B HA H . Matrix Theory Matrix Transposition and Related - 7/30
Transpose and Conjugate Transpose Properties of Transposition For real matrices,the conjugate transpose and the transpose are identical.That is,if AeRmx,then AH =AT. Transposing a matrix twice gives back the original, (AT)T=A,(AH)H=A. Transposition does not affect a scalar, (AA)T=λAT 命电有这女子 Matrix Theory Matrix Transposition and Related -7/30
Transpose and Conjugate Transpose Properties of Transposition ▸ For real matrices, the conjugate transpose and the transpose are identical. That is, if A ∈ R m×n , then A H = A T . ▸ Transposing a matrix twice gives back the original, (A T ) T = A, (A H ) H = A. ▸ Transposition does not affect a scalar, (λA) T = λA T , ▸ The transpose of a sum is the sum of the transposes, (A + B) T = A T + B T , (A + B) H = A H + B H . ▸ The transpose of a product is the product of the transposes with the factors in reverse order, (AB) T = B T A T , (AB) H = B HA H . Matrix Theory Matrix Transposition and Related - 7/30