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Sumario Tipos de Matrices Completo
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En este resumen podrás ver todo sobre las matrices
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TIPOS DE MATRICESMatriz cuadrada: matriz que tiene el mismo 3 2
número de filas que de columnas 5 −1
Matriz identidad o unidad: matriz
cuadrada donde los elementos de la 1 0 0
I= 0 1 0
diagonal principal son unos y el resto
0 0 1
ceros.
Matriz fila: matriz que solo tiene una fila
1 4 −2
1
2
Matriz columna: matriz que solo tiene una
−3
columna
4
0
0 0 0
Matriz nula: todos sus elementos valen cero
0 0 0
Matriz traspuesta de A: es otra matriz At 1 2 −1 1 1 −3
que se obtiene al cambiar en A las filas por A= 1 0 4 At = 2 0 3
las columnas y las columnas por las filas. −3 3 1 −1 4 1
https://marielmatesblog.wordpress.com/
Matriz simétrica: es una matriz cuadrada 4 3 -1
cuyos elementos a ambos lados de la 3 0 -2
diagonal principal son iguales. -1 2 5
Matriz antisimétrica (o hemisimétrica):
matriz cuadrada en la que los elementos a
0 1 −3
ambos lados de la diagonal principal son
−1 0 4
opuestos (iguales pero con distinto
3 −4 0
signo). Los elementos de la diagonal
principal deben ser cero.
4 0 0
Matriz diagonal: matriz cuadrada donde
los elementos que no están en la diagonal 0 0 0
0 0 5
principal son cero.
Matriz triangular superior (inferior): todos los 1 5 −3 1 0 0
elementos por debajo (encima) de la 0 0 4 y −2 1 0
diagonal principal son cero. 0 0 1 3 5 1
, PROPIEDADES DE LAS OPERACIONES CON MATRICES
2 3 3 2 0 1 2 3 3 2 0 1
+ + = + +
1 −1 5 −1 4 −1 1 −1 5 −1 4 −1
ASOCIATIVA
4 0 3 3 −2 1 3 −2 1 4 0 3
0 1 0 + 0 7 0 = 0 7 0 + 0 1 0
0 −1 5 0 0 5 0 0 5 0 −1 5
CONMUTATIVA
1 2 −1 0 0 0 1 2 −1
ELEMENTO
1 0 4 + 0 0 0 = 1 0 4
NEUTRO
−3 3 1 0 0 0 −3 3 1
0 1 −3 0 −1 3 0 0 0
ELEMENTO
−1 0 4 + 1 0 −4 = 0 0 0
OPUESTO
3 −4 0 −3 4 0 0 0 0
1 2 −1 1 2 −1
https://marielmatesblog.wordpress.com/
2· 3· 1 0 4 = 2·3 · 1 0 4
−3 3 1 −3 3 1
ASOCIATIVA
0 1 −3 0 1 −3 0 1 −3
2 − 5 · −1 0 4 = 2 · −1 0 4 +(-5)· −1 0 4
3 −4 0 3 −4 0 3 −4 0
DISTRIBUTIVA 0 1 −3 1 2 −1 0 1 −3 1 2 −1
3· −1 0 4 + 1 0 4 = 3 · −1 0 4 +3· 1 0 4
3 −4 0 −3 3 1 3 −4 0 −3 3 1
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